# csinhf, csinh, csinhl

< c‎ | numeric‎ | complex

C
 Language Headers Type support Program utilities Variadic function support Error handling Dynamic memory management Date and time utilities Strings library Algorithms Numerics Input/output support Localization support Atomic operations (C11) Thread support (C11) Technical Specifications

Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
Hyperbolic functions
 ccosh csinh ctanh

 Defined in header `` float complex       csinhf( float complex z ); (1) (since C99) double complex      csinh( double complex z ); (2) (since C99) long double complex csinhl( long double complex z ); (3) (since C99) Defined in header `` #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.

### Parameters

 z - complex argument

### Return value

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

### 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+∞i`, the result is `±0+NaNi` (the sign of the real part is unspecified) and FE_INVALID is raised
• If `z` is `+0+NaNi`, the result is `±0+NaNi`
• If `z` is `x+∞i` (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 `+∞+0i`, the result is `+∞+0i`
• If `z` is `+∞+yi` (for any positive finite y), the result is `+∞cis(y)`
• If `z` is `+∞+∞i`, the result is `±∞+NaNi` (the sign of the real part is unspecified) and FE_INVALID is raised
• If `z` is `+∞+NaNi`, the result is `±∞+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)