# Scientific/Engineering Functions

## 1/x   Reciprocal

Computes the reciprocal of the number currently displayed.

## 2/ sqrt Square Root

Computes the square root of the number currently displayed.

## x2sqr Square

Computes the square of the number currently displayed.

## log Logarithm to base 10

Computes the logarithm to base 10 of the number currently displayed.

To get the logarithm to any arbitrary base, divide the result by the logarithm of the base. E.g. to get the log to base 2 of 5 use: 5log / 2log = , result:   2.321928    .

## ln Natural Logarithm

Computes the natural logarithm (logarithm to base e) of the number currently displayed.

## xapow X to the Power of a

Computes X to the power of a.

Example:
Calculate 5 raised to the power of 6.

xa   6    =

Result: 15625.000000

## a/ root ath Root of X

Computes the ath root of X (i.e. X to the power of the reciprocal of a).

Example:
Calculate the cube root of two:

root   3    =

Result: 1.259921004989

## � /' Input Degrees, Minutes, Seconds (Sexagesimal)

The deg or  � /' button is used to enter an angle in degrees, minutes and seconds (sexagesimal) in the Angle mode. The button replaces the M+ button which appears in Decimal modes.

To enter a number in sexagesimal format, first enter the number of whole degrees, and press deg or  � /'. Then enter the number of minutes and press deg or  � /' again. Finally enter the number of seconds and press  deg or  � /' a final time (this last press can be omitted). If there are no seconds, the last step can be omitted. Similarly if the number is a whole number of degrees, this can be entered directly without using the  deg or  � /' button at all. You can also input a decimal fraction of degrees, for example 1.5, and this will be converted to sexagesimal notation for display.

Arithmetic calculations can be carried out in Angle mode, or the result or number entered can be converted to another format by selecting a different calculator mode. Similarly a number in any other base can be converted to sexagesimal format by selecting the Angle mode.

Selecting  Angle mode automatically selects appropriate properties and units for conversion.

Example:
What is the sine of 17 degrees, 14 minutes and 30 seconds?

First click on shiftAng , select Angle mode in the Mode menu or the keyboard shortcut (Alt Shift A).

1 7   � /' 1 4   � /' 3 0  � /'

Result: 17 � 14' 30"

Click on Dec to change to Decimal mode or use the  Mode menu or the keyboard shortcut (Alt Shift D):

Result: 17.2416666666667

sin

Result: 0.2964026699

## : Input  Hours, Minutes, Seconds (Sexagesimal)

The : button is used to enter a time in hours, minutes and seconds. The button replaces the M+ button which appears in Decimal modes.

To enter a number in sexagesimal format, first enter the number of whole   hours, and press :. Then enter the number of minutes and press : again. Finally, if needed, enter the number of seconds and press :. If the time is a whole number of hours, this can be entered directly without using the : button at all. You can also input a decimal fraction of hours, for example 1.5, and this will be converted to sexagesimal notation for display.

Arithmetic calculations can be carried out in  Time mode, or the result or number entered can be converted to another format by selecting a different calculator mode. Similarly a number in any other base can be converted to sexagesimal format by selecting the Time mode.

Example:

I started work at 08:30 and finished at 18:54, and I took a 45 minute lunch break. How many hours do I put on my time sheet?

First click shift Time or select Time in the  Mode menu, or use the keyboard shortcut (Alt Shift T).

1 8 : 5 4 : - 8 : 3 0 - : 4 5 =

Result: 09:39:00.00

To continue the calculation to accumulate hours for a weekly time sheet, use the m+ button. To convert to a decimal number of hours, select Decimal mode (or Alt Shift D).

## rand Random Number

Generates a pseudo-random number between 0 and 1.  If you need a number corresponding to some other range, multiply by that number.

Example:  Obtain a random number between 0 and 100.

rand X 100 =

## frac Fractional part

Computes the fractional part of a number.

Example: Obtain the fractional part of pi.

shift pi shift frac =

Result: 0.1415926536

## int Integer part

Computes the integer part of a number.

Example: Obtain the integer part of pi.

shift pi shift int =

Result: 3.

## mod Modulo (remainder)

Computes the remainder of a division. This is the shifted version of the divide ( ) button.

Example: What is the remainder of 27 divided by 6.

27 shift mod 6 =

Result: 3.

## sin Sine

Computes the sine of an angle.

## sinh Hyperbolic Sine

Computes the hyperbolic sine of an angle.

## asin Inverse Sine

Computes the arc sine, i.e. the angle for which the sine is the value entered.

## asinh Inverse Hyperbolic Sine

Computes the angle for which the hyperbolic sine is the value entered.

## cos Cosine

Computes the cosine of an angle.

## cosh Hyperbolic Cosine

Computes the hyperbolic cosine of an angle.

## acos Inverse Cosine

Computes the angle for which the cosine is the value entered.

## acosh Inverse Hyperbolic Cosine

Computes the angle for which the hyperbolic cosine is the value entered.

## tan Tangent

Computes the tangent of an angle.

## tanh Hyperbolic Tangent

Computes the hyperbolic tangent of an angle.

## atan Inverse Tangent

Computes the angle for which the tangent is the value entered.

## atanh Inverse Hyperbolic Tangent

Computes the angle for which the hyperbolic tangent is the value entered.

## x! Factorial

Computes the factorial of a current number. If the current number displayed is not an integer, the result is the factorial of the integer value of the current number.

## pi Pi ratio

Enters the value of pi, the ratio of the circumference of a circle to it's diameter, in the display.

## 10a 10^a Inverse Logarithm

Computes 10 raised to the power of the current number, giving the inverse logarithm (antilogarithm).

To compute the antilogarithm to any base, use the x^a button where x is the base. For example: to find the base 2 antilogarithm of 2.3219280949 enter "2 x^a 2.3219280949 =", result: 5.

## ea Inverse Natural Logarithm

Computes the value of e raised to the power of the current number (exponential function or inverse of natural logarithm).

## +/- Sign

Changes the sign of the number currently displayed.

## < Backspace

Use this button to remove the most recently entered numbers, digit by digit.

To remove the whole of an entry, use CE (Clear entry).

## ( Left Parenthesis

The ( and ) buttons are used to enforce the order of evaluation of an expression. For example, the expression 1 + 2 X 3 would be evaluated as 9 if operator precedence is determined by the order of entry (e.g. using As Entered logic). This is a different answer to the same expression evaluated using algebraic precedence or in a programming language such as BASIC, C or FORTRAN, which gives multiplication and division precedence over addition and subtraction.

To force the calculator to evaluate a particular expression first, use parentheses (brackets). Evaluating 1 + (2 X 3) always gives the result 7, regardless of whether As Entered or Algebraic logic is selected.

See ).

## ) Right Parenthesis

Closes a level of parentheses. The current level of parentheses is shown in the button legend.

See (.