# 3.9 Standard Mathematical Functions

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

### `function`tanargβ

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

### `function`asinargβ

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`acosargβ

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`atany \&optional xβ

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`expargβ

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

### `function`logarg \&optional baseβ

This function returns the logarithm of `arg`, with base `base`. If you donβt specify `base`, the natural base e is used. If `arg` or `base` is negative, `log` returns a NaN.

### `function`exptx yβ

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`sqrtargβ

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-eβ

The mathematical constant e (2.71828β¦).

### `variable`float-piβ

The mathematical constant pi (3.14159β¦).