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Showing content from https://en.cppreference.com/w/cpp/language/../../cpp/../c/header/../numeric/complex/csinh.html below:

csinhf, csinh, csinhl - cppreference.com

(1) (since C99) (2) (since C99) (3) (since C99)

#define sinh( z )

(4) (since C99)

1-3) Computes the complex hyperbolic sine of z.

4)

Type-generic macro: If

z

has type

long double complex

csinhl

is called. if

z

has type

double complex

csinh

is called, if

z

has type

float complex

csinhf

is called. If

z

is real or integer, then the macro invokes the corresponding real function (

sinhf

sinh

sinhl

). If

z

is imaginary, then the macro invokes the corresponding real version of the function

sin

, implementing the formula

sinh(iy) = i sin(y)

, and the return type is imaginary.

[edit] Parameters [edit] Return value

If no errors occur, complex hyperbolic sine of z is returned

[edit] Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

csinh(conj(z)) == conj(csinh(z))
csinh(z) == -csinh(-z)
If z is +0+0i, the result is +0+0i
If z is +0+âi, the result is Â±0+NaNi (the sign of the real part is unspecified) and FE_INVALID is raised
If z is +0+NaNi, the result is Â±0+NaNi
If z is x+âi (for any positive finite x), the result is NaN+NaNi and FE_INVALID is raised
If z is x+NaNi (for any positive finite x), the result is NaN+NaNi and FE_INVALID may be raised
If z is +â+0i, the result is +â+0i
If z is +â+yi (for any positive finite y), the result is +âcis(y)
If z is +â+âi, the result is Â±â+NaNi (the sign of the real part is unspecified) and FE_INVALID is raised
If z is +â+NaNi, the result is Â±â+NaNi (the sign of the real part is unspecified)
If z is NaN+0i, the result is NaN+0i
If z is NaN+yi (for any finite nonzero y), the result is NaN+NaNi and FE_INVALID may be raised
If z is NaN+NaNi, the result is NaN+NaNi

where cis(y) is cos(y) + i sin(y)

[edit] Notes

Mathematical definition of hyperbolic sine is

sinh z =

Hyperbolic sine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi

[edit] Example

#include <stdio.h>
#include <math.h>
#include <complex.h>
 
int main(void)
{
    double complex z = csinh(1);  // behaves like real sinh along the real line
    printf("sinh(1+0i) = %f%+fi (sinh(1)=%f)\n", creal(z), cimag(z), sinh(1));
 
    double complex z2 = csinh(I); // behaves like sine along the imaginary line
    printf("sinh(0+1i) = %f%+fi ( sin(1)=%f)\n", creal(z2), cimag(z2), sin(1));
}

Output:

sinh(1+0i) = 1.175201+0.000000i (sinh(1)=1.175201)
sinh(0+1i) = 0.000000+0.841471i ( sin(1)=0.841471)

[edit] References

C11 standard (ISO/IEC 9899:2011):

7.3.6.5 The csinh functions (p: 194)

7.25 Type-generic math <tgmath.h> (p: 373-375)

G.6.2.5 The csinh functions (p: 541-542)

G.7 Type-generic math <tgmath.h> (p: 545)

C99 standard (ISO/IEC 9899:1999):

7.3.6.5 The csinh functions (p: 175-176)

7.22 Type-generic math <tgmath.h> (p: 335-337)

G.6.2.5 The csinh functions (p: 476-477)

G.7 Type-generic math <tgmath.h> (p: 480)

[edit] See also

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