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## 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 19.4 Exponentiation 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.

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