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 positive, the result is an integer; in this case, overflow causes truncation, 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…).