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# HP Calculators - Mathematical Questions

Overview
This document addresses mathematical questions for the HP 10b, 10bii, 12c, 17bii, 19bii, 20s, 32sii, 38g, 48gx, 48g+, and 49g calculators.
Calculator Symbol Key
The procedures in this document use the following text to represent symbol keys:
 Key Description Text representation Right shift key RS Left-shift key LS colored key; shift key SHIFT Move cursor left cursor-left Move cursor right cursor-right Move cursor up cursor-up Move cursor down cursor-down Backspace/clear backspace Symbol for pi pi x root of y xROOTy
Wrong number for NVP
HP 12c, 17bii, and 19bii
Make sure that the discount rate entered is periodic. The number of periods per year cannot be set in a cash flow, so the annual rate needs to be divided by the number of periods per year (four quarterly, two for semi-annual, and so on).
HP 10b
Make sure that the discount rate that was entered is annualized by multiplying the periodic rate by the number of periods per year (four quarterly, two for semi-annual, and so on).
Calculating the 4th and 5th root of a number
HP 10b
To calculate the 4th root of 81:
1. Press 81, SHIFT, then y^x
2. Press SHIFT, [(], then 4
3. Press SHIFT, 1/x, SHIFT, then [)]
4. Press the = sign
HP 12c
To calculate the 4th root of 81:
1. Press 81, then ENTER
2. Press 4, [1/x], then [y^x]
HP 17bii
To calculate the 4th root of 81:
In Algebraic mode:
1. Press 81, SHIFT, then [y^x]
2. Press 4, SHIFT, [1/x]
3. Press INPUT or the = sign
In RPN mode:
1. Press 81, then INPUT
2. Press 4, SHIFT, [1/x], SHIFT, then [y^x]
HP 19bii
To calculate the 4th root of 81:
In Algebraic mode:
1. Press 81, SHIFT, then [^]
2. Press 4, SHIFT, [1/x]
3. Press INPUT or the = sign
In RPN mode:
1. Press 81, then INPUT
2. Press 4, SHIFT, [1/x], SHIFT, then [^]
Calculating sin (or tangent) of pi Radians Displays Number Other than 0
HP 20s, 32sii, and 19bii
pi cannot be represented exactly with the 12-digit precision of the calculator.
HP 38g
The calculator may not be in the radians mode. If the RAD annunciator is not displayed in the upper left corner of the screen, change the angle mode. Regardless, the HP 38g, like all calculators, can compute using only a finite number of decimal places. Any result involving pi that contains an infinite number of decimal places must be truncated. In this case the rounded number differs from the theoretical answer by one part in 10E 12.
HP 49g
The HP 49g must be in the radians mode since sine (3.1415 degrees) is not zero. If the RAD annunciator does not appear at the top left of the display, press the MODE key, and change the angle measure of the radians. Next, press CAS and clear (that is un-check) the NUMERIC and APPROX fields. If this is not done, the 49g will assume that a numeric calculation is wanted, which for an irrational number like pi will always be an approximation if represented in a finite number of decimal places.
Calculating the sine of pi Results in 'sin (pi)' Rather than 0
HP 48gx/48g+
There are two possibilities.
1. The calculator might not be in the RADIANS mode. if the RAD annunciator is not active at the top left hand corner of the display, press LS, then RAD.
2. The HP 48gx and 48g+, like all calculators, can compute using only a finite number of decimal places. Because SIN (pi) contains an infinite number of decimal places, it must be truncated to twelve decimal places. To get zero, make sure that flag -2 is clear (press 2, [+/-], LS, MODES, FLAG, then CF) and use EVAL.
Converting units (49g)
With the 49g in Algebraic mode, use CONVERT (via cursor-right, UNITS, Tools) with two arguments: the current value (with its unit), then a 1 with the target unit. (To avoid implying multiplication, type the underscore, _ , between value and unit.) For example, to convert 100 meters to yards, use CONVERT (100_m, 1_yd) .
In RPN mode, the syntax is 100_m 1_yd CONVERT. (Or, if flag -117 is set, use a menu shortcut: 100_m cursor-left, yd.)
Calculator gives incorrect or unexpected results when using trigonometric functions
HP 19bii
Make sure the calculator is in the correct trigonometric mode. The trigonometric functions and polar/rectangular coordinated conversions involve angles that can be interpreted either as degrees or radians, depending on the current trigonometric mode. the (2pi) annunciator indicates RADIANS mode.
Changing the trigonometric mode:
To change the trigonometric mode:
1. Press SHIFT, then MODES
2. Press D/R and check for the absence of the radians annunciator.
Trigonometric functions
Pressing TRIG displays a menu of trigonometric functions. Angles are interpreted in degrees or radian, depending on the trigonometric mode. The following table contains a list of the trigonometric functions for the HP 19bii and the keys associated with those functions.
 Key(s) Function Key(s) Function SIN Sine ASIN Arc sine COS Cosine ACOS Arc cosine TAN Tangent ATAN Arc tangent
HP 20s
Make sure the calculator is in the correct trigonometric mode. The following is a list of the trigonometric modes for the HP 20s and their keypad shortcuts.
• Degrees mode: Press RS, then DEG
HP 32si
Make sure the calculator is using the correct angular mode. The following is a list of the trigonometric modes for the HP 32sii and their keypad shortcuts.
• Degrees mode: Press LS, MODES, then DG
• Radians mode: Press LS, MODES, then RD
• Grads mode: Press LS, MODES, then GR
HP 38g
The angle mode may be wrong for the particular problem. Check the angle mode annunciator in the upper left corner of the display screen (DEG means degrees, RAD means radians, and GRD means grads). To change the angle mode:
1. Press the SHIFT key, then MODES
2. While highlighting the "ANGLE MEASURE" field, press the CHOOS menu key.
3. Highlight the desired mode, and then press the OK menu key.
HP 48gx/48g+
The angle mode may be wrong for the particular problem. Check the angle mode annunciator (RAD means radians, GRAD means grads, and NONE means degrees. Press LS, then RAD or use the RS, MODES screen to change the angle mode.
When (-1)^(2/3) is computed the calculator gives a complex number instead of 1 (48g series)
The HP 48g is designed to return the complex principle solution for any fractional exponent. To get the real number root, compute the radicand first (-1^2) using the x^2 key then compute the cube root using the xROOTy key. An algebraic object such as 'XROOT (3 (-1)^2)' can be used as well. Once the algebraic object has been entered, press EVAL to calculate the answer.
Taking the log of a base other than 10 (38g)
To take the log of a base other than 10 use the following formula: if Y=LOGx(Z), then Y=LOG10(Z)(LOG10(X) For example, the LOG2(8) is LOG10(8) divided by LOG10(2), which is 3. The same formula applies to natural logarithms.
IRR/ YR is larger than expected (10bii)
This is IRR per year. To see a periodic IRR, divide IRR/YR by P/ YR.
Some variables used earlier cannot be found (48g series)
Variables in a different directory may have been used. Check all the directories in the calculator.

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