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3.9 Standard Mathematical Functions

These mathematical functions allow integers as well as floating-point numbers as arguments.

function sin arg​

function cos arg​

function tan arg​

These are the basic trigonometric functions, with argument arg measured in radians.

function asin arg​

The value of (asin arg) is a number between -pi/2 and pi/2 (inclusive) whose sine is arg. If arg is out of range (outside [-1, 1]), asin returns a NaN.

function acos arg​

The value of (acos arg) is a number between 0 and pi (inclusive) whose cosine is arg. If arg is out of range (outside [-1, 1]), acos returns a NaN.

function atan y \&optional x​

The value of (atan y) is a number between -pi/2 and pi/2 (exclusive) whose tangent is y. If the optional second argument x is given, the value of (atan y x) is the angle in radians between the vector [x, y] and the X axis.

function exp arg​

This is the exponential function; it returns e to the power arg.

function log arg \&optional base​

This function returns the logarithm of arg, with base base. If you don’t specify base, the natural base e is used. If arg or base is negative, log returns a NaN.

function expt x y​

This function returns x raised to power y. If both arguments are integers and y is nonnegative, the result is an integer; in this case, overflow signals an error, so watch out. If x is a finite negative number and y is a finite non-integer, expt returns a NaN.

function sqrt arg​

This returns the square root of arg. If arg is finite and less than zero, sqrt returns a NaN.

In addition, Emacs defines the following common mathematical constants:

variable float-e​

The mathematical constant e (2.71828…).

variable float-pi​

The mathematical constant pi (3.14159…).