Inverse Trigonometric Functions

These are the usual arc sine, arc cosine and arc tangent functions, which are the inverses of the sine, cosine and tangent functions respectively.

double function>asin/function> (double x) float function>asinf/function> (float x) long double function>asinl/function> (long double x) These functions compute the arc sine of x--that is, the value whose sine is x. The value is in units of radians. Mathematically, there are infinitely many such values; the one actually returned is the one between -pi/2 and pi/2 (inclusive).

The arc sine function is defined mathematically only over the domain -1 to 1. If x is outside the domain, asin signals a domain error.

double function>acos/function> (double x) float function>acosf/function> (float x) long double function>acosl/function> (long double x) These functions compute the arc cosine of x--that is, the value whose cosine is x. The value is in units of radians. Mathematically, there are infinitely many such values; the one actually returned is the one between 0 and pi (inclusive).

The arc cosine function is defined mathematically only over the domain -1 to 1. If x is outside the domain, acos signals a domain error.

double function>atan/function> (double x) float function>atanf/function> (float x) long double function>atanl/function> (long double x) These functions compute the arc tangent of x--that is, the value whose tangent is x. The value is in units of radians. Mathematically, there are infinitely many such values; the one actually returned is the one between -pi/2 and pi/2 (inclusive).

double function>atan2/function> (double y, double x) float function>atan2f/function> (float y, float x) long double function>atan2l/function> (long double y, long double x) This function computes the arc tangent of y/x, but the signs of both arguments are used to determine the quadrant of the result, and x is permitted to be zero. The return value is given in radians and is in the range -pi to pi, inclusive.

If x and y are coordinates of a point in the plane, atan2 returns the signed angle between the line from the origin to that point and the x-axis. Thus, atan2 is useful for converting Cartesian coordinates to polar coordinates. (To compute the radial coordinate, use hypot; see the section called “Exponentiation and Logarithms”.)

If both x and y are zero, atan2 returns zero.

ISO C99 defines complex versions of the inverse trig functions.

complex double function>casin/function> (complex double z) complex float function>casinf/function> (complex float z) complex long double function>casinl/function> (complex long double z) These functions compute the complex arc sine of z--that is, the value whose sine is z. The value returned is in radians.

Unlike the real-valued functions, casin is defined for all values of z.

complex double function>cacos/function> (complex double z) complex float function>cacosf/function> (complex float z) complex long double function>cacosl/function> (complex long double z) These functions compute the complex arc cosine of z--that is, the value whose cosine is z. The value returned is in radians.

Unlike the real-valued functions, cacos is defined for all values of z.

complex double function>catan/function> (complex double z) complex float function>catanf/function> (complex float z) complex long double function>catanl/function> (complex long double z) These functions compute the complex arc tangent of z--that is, the value whose tangent is z. The value is in units of radians.