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hp 39g+ graphing calculator
user’s guide
H
Edition 2
Part Number F2224-90001

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Notice
REGISTER YOUR PRODUCT AT: www.register.hp.com
THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE
PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT
NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY
OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT
NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A
PARTICULAR PURPOSE.
HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS
OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN
CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE
OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.
© Copyright 1994-1995, 1999-2000, 2003 Hewlett-Packard Development
Company, L.P.
Reproduction, adaptation, or translation of this manual is prohibited without
prior written permission of Hewlett-Packard Company, except as allowed
under the copyright laws.
Hewlett-Packard Company
4995 Murphy Canyon Rd,
Suite 301
San Diego,CA 92123
Printing History
Edition 2 December 2003

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Contents i
Contents
Preface
Manual conventions .............................................................. P-1
Notice .................................................................................P-2
1 Getting started
On/off, cancel operations......................................................1-1
The display ..........................................................................1-2
The keyboard .......................................................................1-3
Menus .................................................................................1-8
Input forms ...........................................................................1-9
Mode settings.....................................................................1-10
Setting a mode...............................................................1-12
Aplets (E-lessons).................................................................1-12
Aplet library ..................................................................1-16
Aplet views....................................................................1-16
Aplet view configuration..................................................1-18
Mathematical calculations....................................................1-19
Using fractions....................................................................1-25
Complex numbers ...............................................................1-29
Catalogs and editors ...........................................................1-30
2 Aplets and their views
Aplet views ..........................................................................2-1
About the Symbolic view ...................................................2-1
Defining an expression (Symbolic view) ..............................2-1
Evaluating expressions ......................................................2-3
About the Plot view...........................................................2-5
Setting up the plot (Plot view setup).....................................2-5
Exploring the graph..........................................................2-7
Other views for scaling and splitting the graph ..................2-14
About the numeric view...................................................2-16
Setting up the table (Numeric view setup) ..........................2-17
Exploring the table of numbers.........................................2-18
Building your own table of numbers..................................2-19
“Build Your Own” menu keys...........................................2-20
Example: plotting a circle ................................................2-21

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ii Contents
3 Function aplet
About the Function aplet........................................................ 3-1
Getting started with the Function aplet ................................ 3-1
Function aplet interactive analysis........................................... 3-9
Plotting a piecewise-defined function ................................ 3-12
4 Parametric aplet
About the Parametric aplet .................................................... 4-1
Getting started with the Parametric aplet............................. 4-1
5 Polar aplet
Getting started with the Polar aplet ......................................... 5-1
6 Sequence aplet
About the Sequence aplet...................................................... 6-1
Getting started with the Sequence aplet .............................. 6-1
7 Solve aplet
About the Solve aplet............................................................ 7-1
Getting started with the Solve aplet .................................... 7-2
Use an initial guess............................................................... 7-5
Interpreting results ................................................................ 7-6
Plotting to find guesses.......................................................... 7-7
Using variables in equations ................................................ 7-10
8 Statistics aplet
About the Statistics aplet........................................................ 8-1
Getting started with the Statistics aplet................................ 8-1
Entering and editing statistical data ........................................ 8-6
Defining a regression model............................................ 8-12
Computed statistics ............................................................. 8-13
Plotting.............................................................................. 8-15
Plot types ...................................................................... 8-16
Fitting a curve to 2VAR data ........................................... 8-17
Setting up the plot (Plot setup view) .................................. 8-18
Trouble-shooting a plot ................................................... 8-18
Exploring the graph ....................................................... 8-19
Calculating predicted values ........................................... 8-20

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Contents iii
9 Inference aplet
About the Inference aplet .......................................................9-1
Getting started with the Inference aplet ...............................9-1
Importing sample statistics from the Statistics aplet ................9-4
Hypothesis tests ....................................................................9-8
One-Sample Z-Test............................................................9-8
Two-Sample Z-Test ............................................................9-9
One-Proportion Z-Test......................................................9-10
Two-Proportion Z-Test ......................................................9-11
One-Sample T-Test ..........................................................9-12
Two-Sample T-Test ..........................................................9-14
Confidence intervals............................................................9-15
One-Sample Z-Interval.....................................................9-15
Two-Sample Z-Interval .....................................................9-16
One-Proportion Z-Interval.................................................9-17
Two-Proportion Z-Interval .................................................9-17
One-Sample T-Interval .....................................................9-18
Two-Sample T-Interval......................................................9-19
10 Using the Finance Solver
Calculating Amortizations................................................10-7
11 Using mathematical functions
Math functions....................................................................11-1
The MATH menu ............................................................11-1
Math functions by category ..................................................11-2
Keyboard functions.........................................................11-3
Calculus functions...........................................................11-6
Complex number functions...............................................11-7
Constants ......................................................................11-8
Hyperbolic trigonometry..................................................11-8
List functions ..................................................................11-9
Loop functions................................................................11-9
Matrix functions ...........................................................11-10
Polynomial functions .....................................................11-10
Probability functions......................................................11-12
Real-number functions ...................................................11-13
Two-variable statistics....................................................11-16
Symbolic functions........................................................11-17
Test functions ...............................................................11-18
Trigonometry functions ..................................................11-19
Symbolic calculations ........................................................11-20
Finding derivatives .......................................................11-21

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iv Contents
12 Variables and memory management
Introduction ....................................................................... 12-1
Storing and recalling variables............................................. 12-2
The VARS menu.................................................................. 12-4
Memory Manager .............................................................. 12-9
13 Matrices
Introduction ....................................................................... 13-1
Creating and storing matrices .............................................. 13-2
Working with matrices ........................................................ 13-4
Matrix arithmetic ................................................................ 13-6
Solving systems of linear equations .................................. 13-8
Matrix functions and commands........................................... 13-9
Argument conventions .................................................. 13-10
Matrix functions........................................................... 13-10
Examples......................................................................... 13-13
14 Lists
Displaying and editing lists.................................................. 14-4
Deleting lists.................................................................. 14-6
Transmitting lists............................................................. 14-6
List functions....................................................................... 14-6
Finding statistical values for list elements................................ 14-9
15 Notes and sketches
Introduction ....................................................................... 15-1
Aplet note view .................................................................. 15-1
Aplet sketch view................................................................ 15-3
The notepad ...................................................................... 15-6

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Contents v
16 Programming
Introduction ........................................................................16-1
Program catalog ............................................................16-2
Creating and editing programs.............................................16-4
Using programs ..................................................................16-7
Customizing an aplet...........................................................16-9
Aplet naming convention...............................................16-10
Example......................................................................16-10
Programming commands....................................................16-13
Aplet commands ..........................................................16-14
Branch commands........................................................16-17
Drawing commands......................................................16-19
Graphic commands ......................................................16-20
Loop commands ...........................................................16-22
Matrix commands.........................................................16-23
Print commands............................................................16-25
Prompt commands ........................................................16-25
Stat-One and Stat-Two commands ..................................16-28
Stat-Two commands ......................................................16-29
Storing and retrieving variables in programs....................16-30
Plot-view variables........................................................16-30
Symbolic-view variables ................................................16-37
Numeric-view variables.................................................16-39
Note variables .............................................................16-42
Sketch variables ...........................................................16-42
17 Extending aplets
Creating new aplets based on existing aplets .........................17-1
Using a customized aplet ................................................17-3
Resetting an aplet................................................................17-3
Annotating an aplet with notes .............................................17-4
Annotating an aplet with sketches .........................................17-4
Downloading e-lessons from the web.....................................17-4
Sending and receiving aplets ...............................................17-4
Sorting items in the aplet library menu list ..............................17-5

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vi Contents
Reference information
Glossary.............................................................................. R-1
Resetting the hp 39g+........................................................... R-3
To erase all memory and reset defaults ............................... R-3
If the calculator does not turn on ........................................ R-4
Operating details ................................................................. R-4
Batteries ......................................................................... R-4
Variables............................................................................. R-6
Home variables ............................................................... R-6
Function aplet variables.................................................... R-7
Parametric aplet variables................................................. R-8
Polar aplet variables ........................................................ R-9
Sequence aplet variables................................................ R-10
Solve aplet variables ...................................................... R-11
Statistics aplet variables.................................................. R-12
MATH menu categories....................................................... R-13
Math functions............................................................... R-13
Program constants.......................................................... R-15
Program commands ....................................................... R-16
Status messages ................................................................. R-17
Limiting Warranty
Service ..........................................................................W-3
Regulatory information.....................................................W-5
Index

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Preface P-1
Preface
The hp 39g+ is a feature-rich graphing calculator. It is
also a powerful mathematics learning tool. The hp 39g+
is designed so that you can use it to explore mathematical
functions and their properties.
You can get more information on the hp 39g+ from
Hewlett-Packard’s Calculators web site. You can
download customized aplets from the web site and load
them onto your calculator. Customized aplets are special
applications developed to perform certain functions, and
to demonstrate mathematical concepts.
Hewlett Packard’s Calculators web site can be found at:
http://www.hp.com/calculators
Manual conventions
The following conventions are used in this manual to
represent the keys that you press and the menu options
that you choose to perform the described operations.
• Key presses are represented as follows:
, , , etc.
• Shift keys, that is the key functions that you access by
pressing the key first, are represented as
follows:
CLEAR, MODES, ACOS, etc.
• Numbers and letters are represented normally, as
follows:
5, 7, A, B, etc.
• Menu options, that is, the functions that you select
using the menu keys at the top of the keypad are
represented as follows:
, , .
• Input form fields and choose list items are represented
as follows:
Function, Polar, Parametric
• Your entries as they appear on the command line or
within input forms are represented as follows:
2*X2-3X+5

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P-2 Preface
Notice
This manual and any examples contained herein are
provided as-is and are subject to change without notice.
Except to the extent prohibited by law, Hewlett-Packard
Company makes no express or implied warranty of any
kind with regard to this manual and specifically disclaims
the implied warranties and conditions of merchantability
and fitness for a particular purpose and Hewlett-Packard
Company shall not be liable for any errors or for
incidental or consequential damage in connection with
the furnishing, performance or use of this manual and the
examples herein.
Copyright 2003 Hewlette-Packard Development
Company, L.P.
The programs that control your hp 39g+ are copyrighted
and all rights are reserved. Reproduction, adaptation, or
translation of those programs without prior written
permission from Hewlett-Packard Company is also
prohibited.

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Getting started 1-1
1
Getting started
On/off, cancel operations
To turn on Press to turn on the calculator.
To cancel When the calculator is on, the key cancels the
current operation.
To turn off Press OFF to turn the calculator off.
To save power, the calculator turns itself off after several
minutes of inactivity. All stored and displayed information
is saved.
If you see the ((•)) annunciator or the Low Bat message,
then the calculator needs fresh batteries.
HOME is the calculator’s home view and is common to all
aplets. If you want to perform calculations, or you want to
quit the current activity (such as an aplet, a program, or
an editor), press . All mathematical functions are
available in the HOME. The name of the current aplet is
displayed in the title of the home view.

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1-2 Getting started
The display
To adjust the
contrast
Simultaneously press and (or ) to increase (or
decrease) the contrast.
To clear the display • Press CANCEL to clear the edit line.
• Press CLEAR to clear the edit line and the
display history.
Parts of the
display
Menu key or soft key labels. The labels for the menu
keys’ current meanings. is the label for the first
menu key in this picture. “Press ” means to press the
first menu key, that is, the leftmost top-row key on the
calculator keyboard.
Edit line. The line of current entry.
History. The HOME display ( ) shows up to four
lines of history: the most recent input and output. Older
lines scroll off the top of the display but are retained in
memory.
Title. The name of the current aplet is displayed at the top
of the HOME view. RAD, GRD, DEG specify whether
Radians, Grads or Degrees angle mode is set for HOME.
The T and S symbols indicate whether there is more
history in the HOME display. Press the and to
scroll in the HOME display.
N O T E This user’s guide contains images from the hp 39g+ and
do not display the menu key label.
Title
Edit line
History
Menu key
labels

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Getting started 1-3
Annunciators. Annunciators are symbols that appear
above the title bar and give you important status
information.
The keyboard
Menu keys
Annunciator Description
Shift in effect for next keystroke.
To cancel, press again.
α Alpha in effect for next keystroke.
To cancel, press again.
((•)) Low battery power.
Busy.
Data is being transferred via
infrared or cable.
Menu Key
Labels
Menu Keys
Cursor
Aplet Control
Alpha Key
Shift Key
Enter
Keys
Key
Keys

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1-4 Getting started
• On the calculator keyboard, the top row of keys are
called menu keys. Their meanings depend on the
context—that’s why their tops are blank. The menu
keys are sometimes called “soft keys”.
• The bottom line of the display shows the labels for the
menu keys’ current meanings.
Aplet control keys
The aplet control keys are:
Key Meaning
Displays the Symbolic view for the
current aplet. See “Symbolic view”
on page 1-16.
Displays the Plot view for the current
aplet. See “Plot view” on page 1-17.
Displays the Numeric view for the
current aplet. See “Numeric view” on
page 1-17.
Displays the HOME view. See
“HOME is the calculator’s home view
and is common to all aplets. If you
want to perform calculations, or you
want to quit the current activity (such
as an aplet, a program, or an editor),
press . All mathematical functions are
available in the HOME. The name of
the current aplet is displayed in the
title of the home view.” on page 1-1.
Displays the Aplet Library menu. See
“Aplet library” on page 1-16.
Displays the VIEWS menu. See
“Aplet views” on page 1-16.

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Getting started 1-5
Entry/Edit keys
The entry and edit keys are:
Key Meaning
(CANCEL) Cancels the current operation if the
calculator is on by pressing .
Pressing , then OFF turns the
calculator off.
Accesses the function printed in blue
above a key.
Returns to the HOME view, for
performing calculations.
Accesses the alphabetical
characters printed in orange below
a key. Hold down to enter a string
of characters.
Enters an input or executes an
operation. In calculations,
acts like “=”. When or
is present as a menu key,
acts the same as pressing or
.
Enters a negative number. To enter
–25, press 25. Note: this is not
the same operation that the subtract
button performs ( ).
Enters the independent variable by
inserting X, T, θ, or N into the edit
line, depending on the current
active aplet.
Deletes the character under the
cursor. Acts as a backspace key if
the cursor is at the end of the line.
CLEAR Clears all data on the screen. On a
settings screen, for example Plot
Setup, CLEAR returns all
settings to their default values.
, , , Moves the cursor around the
display. Press first to move to
the beginning, end, top or bottom.

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1-6 Getting started
Shifted keystrokes
There are two shift keys that you use to access the
operations and characters printed above the keys:
and .
CHARS Displays a menu of all available
characters. To type one, use the
arrow keys to highlight it, and press
. To select multiple characters,
select each and press , then
press .
Key Meaning (Continued)
Key Description
Press the key to access the
operations printed in blue above the
keys. For instance, to access the
Modes screen, press , then
press . (MODES is labeled in
blue above the key). You do
not need to hold down when
you press HOME. This action is
depicted in this manual as “press
MODES.”
To cancel a shift, press again.
The alphabetic keys are also shifted
keystrokes. For instance, to type Z,
press Z. (The letters are
printed in orange to the lower right of
each key.)
To cancel Alpha, press
again.
For a lower case letter, press
.
For a string of letters, hold down
while typing.

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Getting started 1-7
HELPWITH The hp 39g+ built-in help is available in HOME only. It
provides syntax help for built-in math functions.
Access the HELPWITH command by pressing
SYNTAX and then the math key for which you require
syntax help.
Example Press SYNTAX
Note: Remove the left parenthesis from built-in
functions such as sine, cosine, and tangent before
invoking the HELPWITH command.
Math keys HOME ( ) is the place to do calculations.
Keyboard keys. The most common operations are
available from the keyboard, such as the arithmetic (like
) and trigonometric (like ) functions. Press
to complete the operation: 256
displays 16.
.
MATH menu. Press
to open the MATH
menu. The MATH menu is a
comprehensive list of math
functions that do not appear
on the keyboard. It also
includes categories for all other functions and constants.
The functions are grouped by category, ranging in
alphabetical order from Calculus to Trigonometry.
• The arrow keys scroll through the list ( , )
and move from the category list in the left column
to the item list in the right column ( , ).
• Press to insert the selected command onto the
edit line.
• Press to dismiss the MATH menu without
selecting a command.
• Pressing displays the list of Program
Constants. You can use these in programs that
you develop.

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1-8 Getting started
• Pressing takes you to the beginning of the
MATH menu.
See “Math functions by category” on page 11-2 for
details of the math functions.
H I N T When using the MATH menu, or any menu on the hp
39g+, pressing an alpha key takes you straight to the first
menu option beginning with that alpha character. With
this method, you do not need to press first. Just
press the key that corresponds to the command’s
beginning alpha character.
Program
commands
Pressing CMDS displays the list of Program
Commands. See “Programming commands” on
page 16-13.
Inactive keys If you press a key that does not operate in the current
context, a warning symbol like this appears. There is
no beep.
Menus
A menu offers you a choice
of items. Menus are
displayed in one or two
columns.
• The arrow in the
display means more
items below.
• The arrow in the
display means more items above.
To search a menu • Press or to scroll through the list. If you press
or , you’ll go all the way to
the end or the beginning of the list. Highlight the item
you want to select, then press (or ).
!

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Getting started 1-9
• If there are two columns, the left column shows
general categories and the right column shows
specific contents within a category. Highlight a
general category in the left column, then highlight an
item in the right column. The list in the right column
changes when a different category is highlighted.
Press or when you have highlighted your
selection.
• To speed-search a list, type the first letter of the word.
For example, to find the Matrix category in ,
press , the Alpha “M” key.
• To go up a page, you can press . To go
down a page, press .
To cancel a menu Press (for CANCEL) or . This cancels the
current operation.
Input forms
An input form shows several fields of information for you
to examine and specify. After highlighting the field to
edit, you can enter or edit a number (or expression). You
can also select options from a list ( ). Some input
forms include items to check ( ). See below for
examples input forms.
Reset input form
values
To reset a field to its default values in an input form, move
the cursor to that field and press . To reset all default
field values in the input form, press CLEAR.

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1-10 Getting started
Mode settings
You use the Modes input form to set the modes for HOME.
H I N T Although the numeric setting in Modes affects only
HOME, the angle setting controls HOME and the current
aplet. The angle setting selected in Modes is the angle
setting used in both HOME and current aplet. To further
configure an aplet, you use the SETUP keys (
and ).
Press MODES to access the HOME MODES input
form.
Setting Options
Angle
Measure
Angle values are:
Degrees. 360 degrees in a circle.
Radians. 2π radians in a circle.
Grads. 400 grads in a circle.
The angle mode you set is the angle
setting used in both HOME and the
current aplet. This is done to ensure
that trigonometric calculations done in
the current aplet and HOME give the
same result.

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Getting started 1-11
Number
Format
The number format mode you set is the
number format used in both HOME
and the current aplet.
Standard. Full-precision display.
Fixed. Displays results rounded to a
number of decimal places. Example:
123.456789 becomes 123.46 in
Fixed 2 format.
Scientific. Displays results with an
exponent, one digit to the left of the
decimal point, and the specified
number of decimal places. Example:
123.456789 becomes 1.23E2 in
Scientific 2 format.
Engineering. Displays result with an
exponent that is a multiple of 3, and
the specified number of significant
digits beyond the first one. Example:
123.456E7 becomes 1.23E9 in
Engineering 2 format.
Fraction. Displays results as fractions
based on the specified number of
decimal places. Examples:
123.456789 becomes 123 in
Fraction 2 format, and .333 becomes
1/3 and 0.142857 becomes 1/7.
See “Using fractions” on page 1-25.
Decimal
Mark
Dot or Comma. Displays a number
as 12456.98 (Dot mode) or as
12456,98 (Comma mode). Dot mode
uses commas to separate elements in
lists and matrices, and to separate
function arguments. Comma mode
uses periods (dot) as separators in
these contexts.
Setting Options (Continued)

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1-12 Getting started
Setting a mode
This example demonstrates how to change the angle
measure from the default mode, radians, to degrees for
the current aplet. The procedure is the same for changing
number format and decimal mark modes.
1. Press MODES to open the HOME MODES input
form.
The cursor (highlight) is
in the first field, Angle
Measure.
2. Press to display a
list of choices.
3. Press to select
Degrees, and press
. The angle measure
changes to degrees.
4. Press to return to
HOME.
H I N T Whenever an input form has a list of choices for a field,
you can press to cycle through them instead of using
.
Aplets (E-lessons)
Aplets are the application environments where you
explore different classes of mathematical operations. You
select the aplet that you want to work with.
Aplets come from a variety of sources:
• Built-in the hp 39g+ (initial purchase).
• Aplets created by saving existing aplets, which have
been modified, with specific configurations. See
“Creating new aplets based on existing aplets” on
page 17-1.
• Downloaded from HP’s Calculators web site.

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Getting started 1-13
• Copied from another calculator.
Aplets are stored in the Aplet
library. See “Aplet library”
on page 1-16 for further
information.
You can modify
configuration settings for the graphical, tabular, and
symbolic views of the aplets in the following table. See
“Aplet view configuration” on page 1-18 for further
information.
In addition to these aplets, which can be used in a variety
of applications, the hp 39g+ is supplied with two
teaching aplets: Quad Explorer and Trig Explorer. You
cannot modify configuration settings for these aplets.
Aplet
name
Use this aplet to explore:
Function Real-valued, rectangular functions y in
terms of x. Example: .
Inference Confidence intervals and Hypothesis
tests based on the Normal and
Students-t distributions.
Parametric Parametric relations x and y in terms of
t. Example: x = cos(t) and y = sin(t).
Polar Polar functions r in terms of an angle θ.
Example: .
Sequence Sequence functions U in terms of n, or
in terms of previous terms in the same or
another sequence, such as and
. Example: ,
and .
Solve Equations in one or more real-valued
variables. Example: .
Statistics One-variable (x) or two-variable (x and
y) statistical data.
y 2x
2
3x 5
+ +
=
r 2 4θ
( )
cos
=
Un 1
–
Un 2
– U1 0
= U2 1
=
Un Un 2
– Un 1
–
+
=
x 1
+ x
2
x
– 2
–
=

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1-14 Getting started
A great many more teaching aplets can be found at HP’s
web site and other web sites created by educators,
together with accompanying documentation, often with
student work sheets. These can be downloaded free of
charge and transferred to the hp 39g+ using the
separately supplied Connectivity Kit.
Quad Explorer
aplet
The Quad Explorer aplet is used to investigate the
behaviour of as the values of a, h and
v change, both by manipulating the equation and seeing
the change in the graph, and by manipulating the graph
and seeing the change in the equation.
H I N T More detailed documentation, and an accompanying
student work sheet can be found at HP’s web site.
Press , select Quad
Explorer, and then press
. The Quad Explorer
aplet opens in
mode, in which the arrow
keys, the and keys,
and the key are used to change the shape of the
graph. This changing shape is reflected in the equation
displayed at the top right corner of the screen, while the
original graph is retained for comparison. In this mode
the graph controls the equation.
It is also possible to have the
equation control the graph.
Pressing displays a
sub-expression of your
equation.
Pressing the and key moves between sub-
expressions, while pressing the and key changes
their values.
Pressing allows the user to select whether all three
sub-expressions will be explored at once or only one at a
time.
y a x h
+
( )
2
v
+
=

##### Page: 24

Getting started 1-15
A button is provided to
evaluate the student’s
knowledge. Pressing
displays a target quadratic
graph. The student must
manipulate the equation’s parameters to make the
equation match the target graph. When a student feels
that they have correctly chosen the parameters a
button evaluates the answer and provide feedback. An
button is provided for those who give up!
Trig Explorer aplet The Trig Explorer aplet is used to investigate the
behaviour of the graph of as the
values of a, b, c and d change, both by manipulating the
equation and seeing the change in the graph, or by
manipulating the graph and seeing the change in the
equation.
Press , select Trig
Explorer, and then press
to display the screen
shown right.
In this mode, the graph
controls the equation.
Pressing the and
keys transforms the
graph, with these
transformations reflected in the equation.
The button labelled is
a toggle between
and . When
is chosen, the ‘point of
control’ is at the origin (0,0)
and the and
keys control vertical and
horizontal transformations. When is chosen the
‘point of control’ is on the first extremum of the graph (i.e.
for the sine graph at .
The arrow keys change the
amplitude and frequency of
the graph. This is most easily
seen by experimenting.
y a bx c
+
( ) d
+
sin
=
Origin
π 2 1
,
⁄
( )
Extremum

##### Page: 25

1-16 Getting started
Pressing displays the
equation at the top of the
screen. The equation is
controlled by the graph.
Pressing the and
keys moves from parameter
to parameter. Pressing the or key changes the
parameter’s values.
The default angle setting for this aplet is radians. The
angle setting can be changed to degrees by pressing
.
Aplet library
Aplets are stored in the Aplet library.
To open an aplet Press to display the Aplet library menu. Select the
aplet and press or .
From within an aplet, you can return to HOME any time
by pressing .
Aplet views
When you have configured an aplet to define the relation
or data that you want to explore, you can display it in
different views. Here are illustrations of the three major
aplet views (Symbolic, Plot, and Numeric), the six
supporting aplet views (from the VIEWS menu), and the
two user-defined views (Note and Sketch).
Symbolic view Press to display the aplet’s Symbolic view.
You use this view to define
the function(s) or equation(s)
that you want to explore.
See “About the Symbolic
view” on page 2-1 for
further information.

##### Page: 26

Getting started 1-17
Plot view Press to display the aplet’s Plot view.
In this view, the functions that
you have defined are
displayed graphically.
See “About the Plot view” on
page 2-5 for further
information.
Numeric view Press to display the aplet’s Numeric view.
In this view, the functions that
you have defined are
displayed in tabular format.
See “About the numeric
view” on page 2-16 for
further information.
Plot-Table view The VIEWS menu contains the Plot-Table view.
Select Plot-Table
Splits the screen into the plot
and the data table. See
“Other views for scaling and
splitting the graph” on
page 2-14 for futher information.
Plot-Detail view The VIEWS menu contains the Plot-Detail view.
Select Plot-Detail
Splits the screen into the plot
and a close-up.
See “Other views for scaling and splitting the graph” on
page 2-14 for further information.

##### Page: 27

1-18 Getting started
Overlay Plot
view
The VIEWS menu contains the Overlay Plot view.
Select Overlay Plot
Plots the current
expression(s) without erasing
any pre-existing plot(s).
See “Other views for scaling and splitting the graph” on
page 2-14 for further information.
Note view Press NOTE to display the aplet’s note view.
This note is transferred with
the aplet if it is sent to
another calculator or to a
PC. A note view contains text
to supplement an aplet.
See “Notes and sketches” on page 15-1 for further
information.
Sketch view Press SKETCH to display the aplet’s sketch view.
Displays pictures to
supplement an aplet.
See “Notes and sketches” on
page 15-1 for further
information.
Aplet view configuration
You use the SETUP keys ( , and
) to configure the aplet. For example, press
SETUP-PLOT ( ) to display the input form for
setting the aplet’s plot settings. Angle measure is
controlled using the MODES view.
Plot Setup Press SETUP-PLOT.
Sets parameters to plot a
graph.

##### Page: 28

Getting started 1-19
Numeric Setup Press SETUP-NUM. Sets
parameters for building a
table of numeric values.
Symbolic Setup This view is only available in
the Statistics aplet in
mode, where it plays an
important role in choosing
data models.
Press SETUP-SYMB.
To change views Each view is a separate environment. To change a view,
select a different view by pressing , ,
keys or select a view from the VIEWS menu. To change
to HOME, press . You do not explicitly close the
current view, you just enter another one—like passing
from one room into another in a house. Data that you
enter is automatically saved as you enter it.
To save aplet
configuration
You can save an aplet configuration that you have used,
and transfer the aplet to other hp 39g+ calculators. See
“Sending and receiving aplets” on page 17-4.
Mathematical calculations
The most commonly used math operations are available
from the keyboard. Access to the rest of the math
functions is via the MATH menu ( ).
To access programming commands, press CMDS.
See “Programming commands” on page 16-13 for
further information.
Where to start The home base for the calculator is the HOME view
( ). You can do all calculations here, and you can
access all operations.
Entering
expressions
• Enter an expression into the hp 39g+ in the same left-
to-right order that you would write the expression.
This is called algebraic entry.
• To enter functions, select the key or MATH menu item
for that function. You can also enter a function by
using the Alpha keys to spell out its name.

##### Page: 29

1-20 Getting started
• Press to evaluate the expression you have in
the edit line (where the blinking cursor is). An
expression can contain numbers, functions, and
variables.
Example Calculate :
Long results If the result is too long to fit on the display line, or if you
want to see an expression in textbook format, press
to highlight it and then press .
Negative
numbers
Type to start a negative number or to insert a
negative sign.
To raise a negative number to a power, enclose it in
parentheses. For example, (–5)2
= 25, whereas –52
=
–25.
Scientific
notation
(powers of 10)
A number like or is written in
scientific notation, that is, in terms of powers of ten. This
is simpler to work with than 50000 or 0.000000321. To
enter numbers like these, use EEX. (This is easier than
using 10 .)
Example Calculate
4 EEX
13
6 EEX
23 3 EEX
5
23
2
14 8
–
3
–
---------------------------
- 45
( )
ln
23
14
8
3
45
5 10
4
× 3.21 10
7
–
×
4 10
13
–
×
( ) 6 10
23
×
( )
3 10
5
–
×
----------------------------------------------------

##### Page: 30

Getting started 1-21
Explicit and
implicit
multiplication
Implied multiplication takes place when two operands
appear with no operator in between. If you enter AB, for
example, the result is A*B.
However, for clarity, it is better to include the
multiplication sign where you expect multiplication in an
expression. It is clearest to enter AB as A*B.
H I N T Implied multiplication will not always work as expected.
For example, entering A(B+4) will not give A*(B+4).
Instead an error message is displayed: “Invalid User
Function”. This is because the calculator interprets
A(B+4) as meaning ‘evaluate function A at the value
B+4’, and function A does not exist. When in doubt, insert
the * sign manually.
Parentheses You need to use parentheses to enclose arguments for
functions, such as SIN(45). You can omit the final
parenthesis at the end of an edit line. The calculator
inserts it automatically.
Parentheses are also important in specifying the order of
operation. Without parentheses, the hp 39g+ calculates
according to the order of algebraic precedence (the next
topic). Following are some examples using parentheses.
Entering... Calculates...
45 π sin (45 + π)
45 π sin (45) + π
85 9
85 9
85 9
×
85 9
×

##### Page: 31

1-22 Getting started
Algebraic
precedence
order of
evaluation
Functions within an expression are evaluated in the
following order of precedence. Functions with the same
precedence are evaluated in order from left to right.
1. Expressions within parentheses. Nested parentheses
are evaluated from inner to outer.
2. Prefix functions, such as SIN and LOG.
3. Postfix functions, such as !
4. Power function, ^, NTHROOT.
5. Negation, multiplication, and division.
6. Addition and subtraction.
7. AND and NOT.
8. OR and XOR.
9. Left argument of | (where).
10.Equals, =.
Largest and
smallest
numbers
The smallest number the hp 39g+ can represent is
1 × 10–499(1E–499). A smaller result is displayed as
zero. The largest number is 9.99999999999 × 10499
(1E499). A greater result is displayed as this number.
Clearing
numbers
• clears the character under the cursor. When the
cursor is positioned after the last character,
deletes the character to the left of the cursor, that is, it
performs the same as a backspace key.
• CANCEL ( ) clears the edit line.
• CLEAR clears all input and output in the
display, including the display history.
Using previous
results
The HOME display ( ) shows you four lines of
input/output history. An unlimited (except by memory)
number of previous lines can be displayed by scrolling.
You can retrieve and reuse any of these values or
expressions.
Output
Last output
Input
Last input
Edit line

##### Page: 32

Getting started 1-23
When you highlight a previous input or result (by pressing
), the and menu labels appear.
To copy a previous
line
Highlight the line (press ) and press . The
number (or expression) is copied into the edit line.
To reuse the last
result
Press ANS (last answer) to put the last result from the
HOME display into an expression. ANS is a variable that
is updated each time you press .
To repeat a
previous line
To repeat the very last line, just press . Otherwise,
highlight the line (press ) first, and then press .
The highlighted expression or number is re-entered. If the
previous line is an expression containing the ANS, the
calculation is repeated iteratively.
Example See how ANS retrieves and reuses the last result
(50), and updates ANS (from 50 to 75 to 100).
50 25
You can use the last result as the first expression in the edit
line without pressing ANS. Pressing , , , or
, (or other operators that require a preceding
argument) automatically enters ANS before the operator.
You can reuse any other expression or value in the HOME
display by highlighting the expression (using the arrow
keys), then pressing . See “Using previous results”
on page 1-22 for more details.
The variable ANS is different from the numbers in HOME’s
display history. A value in ANS is stored internally with the
full precision of the calculated result, whereas the
displayed numbers match the display mode.

##### Page: 33

1-24 Getting started
H I N T When you retrieve a number from ANS, you obtain the
result to its full precision. When you retrieve a number
from the HOME’s display history, you obtain exactly what
was displayed.
Pressing evaluates (or re-evaluates) the last input,
whereas pressing ANS copies the last result (as ANS)
into the edit line.
Storing a value
in a variable
You can save an answer in a variable and use the
variable in later calculations. There are 27 variables
available for storing real values. These are A to Z and θ.
See Chapter 12, “Variables and memory management”
for more information on variables. For example:
1. Perform a calculation.
45 8 3
2. Store the result in the A variable.
A
3. Perform another calculation using the A variable.
95 2 A

##### Page: 34

Getting started 1-25
Accessing the
display history
Pressing enables the highlight bar in the display
history. While the highlight bar is active, the following
menu and keyboard keys are very useful:
Clearing the
display history
It’s a good habit to clear the display history (
CLEAR) whenever you have finished working in HOME. It
saves calculator memory to clear the display history.
Remember that all your previous inputs and results are
saved until you clear them.
Using fractions
To work with fractions in HOME, you set the number
format to Fractions, as follows:
Setting Fraction
mode
1. In HOME, open the HOME MODES input form.
MODES
Key Function
, Scrolls through the display history.
Copies the highlighted expression to
the position of the cursor in the edit line.
Displays the current expression in
standard mathematical form.
Deletes the highlighted expression from
the display history, unless there is a
cursor in the edit line.
CLEAR
Clears all lines of display history and
the edit line.

##### Page: 35

1-26 Getting started
2. Select Number Format, press to display the
options, and highlight Fraction.
3. Press to select the Number Format option, then
move to the precision value field.
4. Enter the precision value that you want to use, and
press to set the precision. Press to return
to HOME.
See “Setting fraction precision” below for more
information.
Setting fraction
precision
The fraction precision setting determines the precision in
which the hp 39g+ converts a decimal value to a fraction.
The greater the precision value that is set, the closer the
fraction is to the decimal value.
By choosing a precision of 1 you are saying that the
fraction only has to match 0.234 to at least 1 decimal
place (3/13 is 0.23076...).
The fractions used are found using the technique of
continued fractions.
When converting recurring decimals this can be
important. For example, at precision 6 the decimal
0.6666 becomes 3333/5000 (6666/10000) whereas
at precision 3, 0.6666 becomes 2/3, which is probably
what you would want.
For example, when converting .234 to a fraction, the
precision value has the following effect:

##### Page: 36

Getting started 1-27
• Precision set to 1:
• Precision set to 2:
• Precision set to 3:
• Precision set to 4
Fraction
calculations
When entering fractions:
• You use the key to separate the numerator part
and the denominator part of the fraction.
• To enter a mixed fraction, for example, 11
/2 , you
enter it in the format (1+1/2).
For example, to perform the following calculation:
3(23
/4 + 57
/8)
1. Set the Number format mode to Fraction and
specify a precision value of 4. Select Fraction
MODES
Select
Fraction
4

##### Page: 37

1-28 Getting started
2. Enter the calculation.
3 2 3
4 5 7
8
Note: Ensure you are in
the HOME view.
3. Evaluate the calculation.
Converting
decimals to
fractions
To convert a decimal value to a fraction:
1. Set the number format mode to Fraction.
2. Either retrieve the value from the History, or enter the
value on the command line.
3. Press to convert the number to a fraction.
When converting a decimal to a fraction, keep the
following points in mind:
• When converting a recurring decimal to a fraction,
set the fraction precision to about 6, and ensure that
you include more than six decimal places in the
recurring decimal that you enter.
In this example, the
fraction precision is set
to 6. The top
calculation returns the
correct result. The
bottom one does not.
• To convert an exact decimal to a fraction, set the
fraction precision to at least two more than the
number of decimal places in the decimal.
In this example, the
fraction precision is set
to 6.

##### Page: 38

Getting started 1-29
Complex numbers
Complex results The hp 39g+ can return a complex number as a result for
some math functions. A complex number appears as an
ordered pair (x, y), where x is the real part and y is the
imaginary part. For example, entering returns (0,1).
To enter complex
numbers
Enter the number in either of these forms, where x is the
real part, y is the imaginary part, and i is the imaginary
constant, :
• (x, y) or
• x + iy.
To enter i:
• press
or
• press , or keys to select Constant,
to move to the right column of the menu, to
select i, and .
Storing complex
numbers
There are 10 variables available for storing complex
numbers: Z0 to Z9. To store a complex number in a
variable:
• Enter the complex number, press , enter the
variable to store the number in, and press .
4 5
Z 0
1
–
1
–

##### Page: 39

1-30 Getting started
Catalogs and editors
The hp 39g+ has several catalogs and editors. You use
them to create and manipulate objects. They access
features and stored values (numbers or text or other items)
that are independent of aplets.
• A catalog lists items, which you can delete or
transmit, for example an aplet.
• An editor lets you create or modify items and
numbers, for example a note or a matrix.
Catalog/Editor Contents
Aplet library
( )
Aplets.
Sketch editor
( SKETCH)
Sketches and diagrams, See
Chapter 15, “Notes and
sketches”.
List ( LIST) Lists. In HOME, lists are
enclosed in {}. See Chapter 14,
“Lists”.
Matrix (
MATRIX)
One- and two-dimensional
arrays. In HOME, arrays are
enclosed in []. See Chapter 13,
“Matrices”.
Notepad (
NOTEPAD)
Notes (short text entries). See
Chapter 15, “Notes and
sketches”.
Program (
PROGRM)
Programs that you create, or
associated with user-defined
aplets. See Chapter 16,
“Programming”.

##### Page: 40

Aplets and their views 2-1
2
Aplets and their views
Aplet views
This section examines the options and functionality of the
three main views for the Function, Polar, Parametric, and
Sequence aplets: Symbolic, Plot, and Numeric views.
About the Symbolic view
The Symbolic view is the defining view for the Function,
Parametric, Polar, and Sequence aplets. The other views
are derived from the symbolic expression.
You can create up to 10 different definitions for each
Function, Parametric, Polar, and Sequence aplet. You
can graph any of the relations (in the same aplet)
simultaneously by selecting them.
Defining an expression (Symbolic view)
Choose the aplet from the Aplet Library.
Press or to
select an aplet.
The Function,
Parametric, Polar, and Sequence aplets start in the
Symbolic view.
If the highlight is on an existing expression, scroll to
an empty line—unless you don’t mind writing over the
expression—or, clear one line ( ) or all lines
( CLEAR).
Expressions are selected (check marked) on entry. To
deselect an expression, press . All selected
expressions are plotted.

##### Page: 41

2-2 Aplets and their views
– For a Function
definition, enter
an expression to
define F(X). The
only independent
variable in the
expression is X.
– For a
Parametric
definition, enter
a pair of
expressions to
define X(T) and
Y(T). The only
independent variable in the expressions is T.
– For a Polar
definition, enter
an expression to
define R(θ). The
only independent
variable in the
expression is θ.
– For a Sequence
definition, either:
Enter the first and
second terms for U
(U1, or...U9, or
U0). Define the nth
term of the
sequence in terms of N or of the prior terms,
U(N–1) and U(N–2). The expressions should
produce real-valued sequences with integer
domains. Or define the nth term as a non-
recursive expression in terms of n only. In this
case, the calculator inserts the first two terms
based on the expression that you define.

##### Page: 42

Aplets and their views 2-3
Evaluating expressions
In aplets In the Symbolic view, a variable is a symbol only, and
does not represent one specific value. To evaluate a
function in Symbolic view, press . If a function calls
another function, then resolves all references to
other functions in terms of their independent variable.
1. Choose the Function
aplet.
Select Function
2. Enter the expressions in the Function aplet’s Symbolic
view.
A
B
F1
F2
3. Highlight F3(X).
4. Press
Note how the values
for F1(X) and F2(X) are
substituted into F3(X).

##### Page: 43

2-4 Aplets and their views
In HOME You can also evaluate any expression in HOME by
entering it into the edit line and pressing .
For example, define F4 as below. In HOME, type
F4(9)and press . This evaluates the expression,
substituting 9 in place of X into F4.
SYMB view keys The following table details the menu keys that you use to
work with the Symbolic view.
Key Meaning
Copies the highlighted expression to
the edit line for editing. Press
when done.
Checks/unchecks the current
expression (or set of expressions).
Only checked expression(s) are
evaluated in the Plot and Numeric
views.
Enters the independent variable in the
Function aplet. Or, you can use the
key on the keyboard.
Enters the independent variable in the
Parametric aplet. Or, you can use the
key on the keyboard.
Enters the independent variable in the
Polar aplet. Or, you can use the
key on the keyboard.
Enters the independent variable in the
Sequence aplet. Or, you can use the
key on the keyboard.
Displays the current expression in text
book form.
Resolves all references to other
definitions in terms of variables and
evaluates all arithmetric expressions.
Displays a menu for entering variable
names or contents of variables.

##### Page: 44

Aplets and their views 2-5
About the Plot view
After entering and selecting (check marking) the
expression in the Symbolic view, press . To adjust
the appearance of the graph or the interval that is
displayed, you can change the Plot view settings.
You can plot up to ten expressions at the same time.
Select the expressions you want to be plotted together.
Setting up the plot (Plot view setup)
Press SETUP-PLOT to define any of the settings
shown in the next two tables.
1. Highlight the field to edit.
– If there is a number to enter, type it in and press
or .
– If there is an option to choose, press ,
highlight your choice, and press or .
As a shortcut to , just highlight the field to
change and press to cycle through the
options.
– If there is an option to select or deselect, press
to check or uncheck it.
2. Press to view more settings.
3. When done, press to view the new plot.
Displays the menu for entering math
operations.
CHARS Displays special characters. To enter
one, place the cursor on it and press
. To remain in the CHARS menu
and enter another special character,
press .
Deletes the highlighted expression or
the current character in the edit line.
CLEAR Deletes all expressions in the list or
clears the edit line.
Key Meaning (Continued)

##### Page: 45

2-6 Aplets and their views
Plot view
settings
The plot view settings are:
Those items with space for a checkmark are settings you
can turn on or off. Press to display the second
page.
Field Meaning
XRNG, YRNG Specifies the minimum and
maximum horizontal (X) and
vertical (Y) values for the plotting
window.
RES For function plots: Resolution;
“Faster” plots in alternate pixel
columns; “Detail” plots in every
pixel column.
TRNG Parametric aplet: Specifies the t-
values (T) for the graph.
θRNG Polar aplet: Specifies the angle (θ)
value range for the graph.
NRNG Sequence aplet: Specifies the
index (N) values for the graph.
TSTEP For Parametric plots: the increment
for the independent variable.
θSTEP For Polar plots: the increment
value for the independent
variable.
SEQPLOT For Sequence aplet: Stairstep or
Cobweb types.
XTICK Horizontal spacing for tickmarks.
YTICK Vertical spacing for tickmarks.
Field Meaning
SIMULT If more than one relation is being
plotted, plots them simultaneously
(otherwise sequentially).
INV. CROSS Cursor crosshairs invert the status
of the pixels they cover.

##### Page: 46

Aplets and their views 2-7
Reset plot
settings
To reset the default values for all plot settings, press
CLEAR in the Plot Setup view. To reset the default
value for a field, highlight the field, and press .
Exploring the graph
Plot view gives you a selection of keys and menu keys to
explore a graph further. The options vary from aplet to
aplet.
PLOT view keys The following table details the keys that you use to work
with the graph.
CONNECT Connect the plotted points. (The
Sequence aplet always connects
them.)
LABELS Label the axes with XRNG and
YRNG values.
AXES Draw the axes.
GRID Draw grid points using XTICK
and YTICK spacing.
Field Meaning (Continued)
Key Meaning
CLEAR Erases the plot and axes.
Offers additional pre-defined views
for splitting the screen and for scaling
(“zooming”) the axes.
Moves cursor to far left or far right.
Moves cursor between relations.
or Interrupts plotting.
Continues plotting if interrupted.

##### Page: 47

2-8 Aplets and their views
Trace a graph You can trace along a function using the or key
which moves the cursor along the graph. The display also
shows the current coordinate position (x, y) of the cursor.
Trace mode and the coordinate display are automatically
set when a plot is drawn.
Note: Tracing might not appear to exactly follow your
plot if the resolution (in Plot Setup view) is set to Faster.
This is because RES: FASTER plots in only every other
column, whereas tracing always uses every column.
In Function and Sequence Aplets: You can also
scroll (move the cursor) left or right beyond the edge of
the display window in trace mode, giving you a view of
more of the plot.
To move between
relations
If there is more than one relation displayed, press or
to move between relations.
Turns menu-key labels on and off.
When the labels are off, pressing
turns them back on.
• Pressing once displays the
full row of labels.
• Pressing a second time
removes the row of labels to
display only the graph.
• Pressing a third time
displays the coordinate mode.
Displays the ZOOM menu list.
Turns trace mode on/off. A white box
appears over the on .
Opens an input form for you to enter
an X (or T or N or θ) value. Enter the
value and press . The cursor jumps
to the point on the graph that you
entered.
Function aplet only: turns on menu list
for root-finding functions (see
“Analyse graph with FCN functions”
on page 3-4).
Displays the current, defining
expression. Press to restore the
menu.
Key Meaning (Continued)

##### Page: 48

Aplets and their views 2-9
To jump directly to
a value
To jump straight to a value rather than using the Trace
function, use the menu key. Press , then enter
a value. Press to jump to the value.
To turn trace on/off If the menu labels are not displayed, press first.
• Turn off trace mode by pressing .
• Turn on trace mode by pressing .
• To turn the coordinate display off, press .
Zoom within a
graph
One of the menu key options is . Zooming redraws
the plot on a larger or smaller scale. It is a shortcut for
changing the Plot Setup.
The Set Factors... option enables you to set the
factors by which you zoom in or zoom out, and whether
the zoom is centered about the cursor.
ZOOM options Press , select an option, and press . (If
is not displayed, press .) Not all options are
available in all aplets.
Option Meaning
Center Re-centers the plot around the
current position of the cursor without
changing the scale.
Box... Lets you draw a box to zoom in on.
See “Other views for scaling and
splitting the graph” on page 2-14.
In Divides horizontal and vertical
scales by the X-factor and Y-factor.
For instance, if zoom factors are 4,
then zooming in results in 1/4 as
many units depicted per pixel. (see
Set Factors...)
Out Multiplies horizontal and vertical
scales by the X-factor and Y-factor
(see Set Factors...).
X-Zoom In Divides horizontal scale only, using
X-factor.
X-Zoom Out Multiplies horizontal scale, using
X-factor.

##### Page: 49

2-10 Aplets and their views
Y-Zoom In Divides vertical scale only, using
Y-factor.
Y-Zoom Out Multiplies vertical scale only, using
Y-factor.
Square Changes the vertical scale to match
the horizontal scale. (Use this after
doing a Box Zoom, X-Zoom, or
Y-Zoom.)
Set
Factors...
Sets the X-Zoom and Y-Zoom factors
for zooming in or zooming out.
Includes option to recenter the plot
before zooming.
Auto Scale Rescales the vertical axis so that the
display shows a representative
piece of the plot, for the supplied x
axis settings. (For Sequence and
Statistics aplets, autoscaling
rescales both axes.)
The autoscale process uses the first
selected function only to determine
the best scale to use.
Decimal Rescales both axes so each pixel =
0.1 units. Resets default values for
XRNG
(–6.5 to 6.5) and YRNG (–3.1 to
3.2). (Not in Sequence or Statistics
aplets.)
Integer Rescales horizontal axis only,
making each pixel =1 unit. (Not
available in Sequence or Statistics
aplets.)
Trig Rescales horizontal axis so
1 pixel = π/24 radians, 7.58, or
81
/3 grads; rescales vertical axis
so
1 pixel = 0.1 unit.
(Not in Sequence or Statistics
aplets.)
Option Meaning (Continued)

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