— Function: int gsl_sf_polar_to_rect (double r, double theta, gsl_sf_result * x, gsl_sf_result * y);

This function converts the polar coordinates (r,theta) to rectilinear coordinates (x,y), x = r\cos(\theta), y = r\sin(\theta).

— Function: int gsl_sf_rect_to_polar (double x, double y, gsl_sf_result * r, gsl_sf_result * theta)

This function converts the rectilinear coordinates (x,y) to polar coordinates (r,theta), such that x = r\cos(\theta), y = r\sin(\theta). The argument theta lies in the range [-\pi, \pi].