To convert a Cartesian co-ordinate pair x,y into polar co-ordinates r (radius) and θ (argument or azimuth):

double x, y;

double r = sqrt(x * x, y * y); // or
double r = hypot(x, y);
double theta = atan2(y, x);

For the inverse conversion:

double r, theta;

double x = r * cos(theta);
double y = r * sin(theta);

One can also convert a pair of Cartesian co-ordinates into a complex number, and use carg and cabs to get the angle and radius.

#include <math.h>
float atan2f(float y, float x);
double atan2(double y, double x);
long double atan2l(long double y, long double x);

#include <tgmath.h>
real-floating-type atan2(real-floating-type y, real-floating-type x);

The atan2 functions take a co-ordinate pair (x, y), and return the angle formed by this point, the origin, and any point on the positive x axis, in the range [−π, +π]. The result has the same sign as y, and a magnitude greater than ½π if x is negative.

#include <math.h>
float hypotf(float x, float y);
double hypot(double x, double y);
long double hypotl(long double x, long double y);

#include <tgmath.h>
real-floating-type hypot(real-floating-type x, real-floating-type y);

The hypot functions take a co-ordinate pair (x, y), and return the distance between this point and the origin, √(x² + y²).