/C

# casinf, casin, casinl

Defined in header `<complex.h>`
`float complex       casinf( float complex z );`
(1) (since C99)
`double complex      casin( double complex z );`
(2) (since C99)
`long double complex casinl( long double complex z );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#define asin( z )`
(4) (since C99)
1-3) Computes the complex arc sine of `z` with branch cuts outside the interval [−1,+1] along the real axis.
4) Type-generic macro: If `z` has type `long double complex`, `casinl` is called. if `z` has type `double complex`, `casin` is called, if `z` has type `float complex`, `casinf` is called. If `z` is real or integer, then the macro invokes the corresponding real function (`asinf`, `asin`, `asinl`). If `z` is imaginary, then the macro invokes the corresponding real version of the function `asinh`, implementing the formula asin(iy) = i asinh(y), and the return type of the macro is imaginary.

### Parameters

 z - complex argument

### Return value

If no errors occur, complex arc sine of `z` is returned, in the range of a strip unbounded along the imaginary axis and in the interval [−π/2; +π/2] along the real axis.

Errors and special cases are handled as if the operation is implemented by `-I * casinh(I*z)`.

Inverse sine (or arc sine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞,-1) and (1,∞) of the real axis.

The mathematical definition of the principal value of arc sine is asin z = -iln(iz + 1-z2
) For any z, asin(z) = acos(-z) -

π/2

### Example

```#include <stdio.h>
#include <math.h>
#include <complex.h>

int main(void)
{
double complex z = casin(-2);
printf("casin(-2+0i) = %f%+fi\n", creal(z), cimag(z));

double complex z2 = casin(conj(-2)); // or CMPLX(-2, -0.0)
printf("casin(-2-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));

// for any z, asin(z) = acos(-z) - pi/2
double pi = acos(-1);
double complex z3 = csin(cacos(conj(-2))-pi/2);
printf("csin(cacos(-2-0i)-pi/2) = %f%+fi\n", creal(z3), cimag(z3));
}```

Output:

```casin(-2+0i) = -1.570796+1.316958i
casin(-2-0i) (the other side of the cut) = -1.570796-1.316958i
csin(cacos(-2-0i)-pi/2) = 2.000000+0.000000i```
• C11 standard (ISO/IEC 9899:2011):
• 7.3.5.2 The casin functions (p: 190)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
• 7.3.5.2 The casin functions (p: 172)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• G.7 Type-generic math <tgmath.h> (p: 480)

 cacoscacosfcacosl (C99)(C99)(C99) computes the complex arc cosine (function) catancatanfcatanl (C99)(C99)(C99) computes the complex arc tangent (function) csincsinfcsinl (C99)(C99)(C99) computes the complex sine (function) asinasinfasinl (C99)(C99) computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function) C++ documentation for `asin`