Inverse Trig Functions - The GNU C Library

Next: Exponents and Logarithms, Previous: Trig Functions, Up: Mathematics

### 19.3 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.

— Function: double asin (double x)

> — Function: float asinf (float x)

> > — Function: long double asinl (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.

— Function: double acos (double x)

> — Function: float acosf (float x)

> > — Function: long double acosl (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.

— Function: double atan (double x)

> — Function: float atanf (float x)

> > — Function: long double atanl (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).

— Function: double atan2 (double y, double x)

> — Function: float atan2f (float y, float x)

> > — Function: long double atan2l (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 Exponents and Logarithms.)

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

ISO C99 defines complex versions of the inverse trig functions.

— Function: complex double casin (complex double z)

> — Function: complex float casinf (complex float z)

> > — Function: complex long double casinl (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.

— Function: complex double cacos (complex double z)

> — Function: complex float cacosf (complex float z)

> > — Function: complex long double cacosl (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.

— Function: complex double catan (complex double z)

> — Function: complex float catanf (complex float z)

> > — Function: complex long double catanl (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.