### 5.6 Inverse Complex Trigonometric Functions

Function: gsl_complex gsl_complex_arcsin (gsl_complex z)

  This function returns the complex arcsine of the complex number z, \arcsin(z). The branch cuts are on the real axis, less than -1 and greater than 1.

Function: gsl_complex gsl_complex_arcsin_real (double z)

  This function returns the complex arcsine of the real number z, \arcsin(z). For z between -1 and 1, the function returns a real value in the range [-\pi/2,\pi/2]. For z less than -1 the result has a real part of -\pi/2 and a positive imaginary part. For z greater than 1 the result has a real part of \pi/2 and a negative imaginary part.

Function: gsl_complex gsl_complex_arccos (gsl_complex z)

  This function returns the complex arccosine of the complex number z, \arccos(z). The branch cuts are on the real axis, less than -1 and greater than 1.

Function: gsl_complex gsl_complex_arccos_real (double z)

  This function returns the complex arccosine of the real number z, \arccos(z). For z between -1 and 1, the function returns a real value in the range [0,\pi]. For z less than -1 the result has a real part of \pi and a negative imaginary part. For z greater than 1 the result is purely imaginary and positive.

Function: gsl_complex gsl_complex_arctan (gsl_complex z)

  This function returns the complex arctangent of the complex number z, \arctan(z). The branch cuts are on the imaginary axis, below -i and above i.

Function: gsl_complex gsl_complex_arcsec (gsl_complex z)

  This function returns the complex arcsecant of the complex number z, \arcsec(z) = \arccos(1/z).

Function: gsl_complex gsl_complex_arcsec_real (double z)

  This function returns the complex arcsecant of the real number z, \arcsec(z) = \arccos(1/z).

Function: gsl_complex gsl_complex_arccsc (gsl_complex z)

  This function returns the complex arccosecant of the complex number z, \arccsc(z) = \arcsin(1/z).

Function: gsl_complex gsl_complex_arccsc_real (double z)

  This function returns the complex arccosecant of the real number z, \arccsc(z) = \arcsin(1/z).

Function: gsl_complex gsl_complex_arccot (gsl_complex z)

  This function returns the complex arccotangent of the complex number z, \arccot(z) = \arctan(1/z).