Question

The problem I’m having is not finding the distance but finding the radians with Atan() and converting it to degrees.

using System;
class Program
{
    static void Main()
    {
        double xCoord =0, yCoord=0 ;       
        //accessing methods
        getUserInput(ref xCoord, ref yCoord);
        CalulatePolarCoords(ref xCoord, ref yCoord);
        outputCords( ref xCoord,  ref yCoord);
        Console.ReadLine();
    }//End Main()

    static void getUserInput(ref double xc, ref double yc) 
    {
    //validating input
        do
        {
            Console.WriteLine(" please enter the x cororidnate must not equal 0 ");
            xc = double.Parse(Console.ReadLine());
            Console.WriteLine("please inter the y coordinate");
            yc = double.Parse(Console.ReadLine());
        if(xc <= 0)
    Console.WriteLine(" invalid input"); 
        }
        while (xc <= 0);
            Console.WriteLine(" thank you");

    }

   //calculating coords
    static void CalulatePolarCoords(ref double x , ref double y) 
    {
        double r;
        double q;
       r = x;
       q = y;
        r = Math.Sqrt((x*x) + (y*y));

        q = Math.Atan(x/y);

    x = r;
    y = q;
    }
    static void outputCords( ref double x, ref double y)
    {
        Console.WriteLine(" The polar cordinates are...");
        Console.WriteLine("distance from the Origin {0}",x);
        Console.WriteLine(" Angle (in degrees) {0}",y);
        Console.WriteLine(" press enter to continute");

    }
}//End class Program

Answer 1

You want to use Atan2 here.

q = Math.Atan2(y, x);

To convert to degrees multiply by 180/Math.PI.

This will give you a result in the range -180 to 180. If you want it in the range 0 to 360 then you will have to shift any negative angles by 360.

I also strongly recommend that you do not return your polar coordinates in the same parameters that you used to pass in cartesian coordinates. Make your function like this:

static void CalculatePolarCoords(double x, double y, out double r, out double q)

Your outputCoords method also uses ref parameters incorrectly. Only use ref parameters for values that are passed into a method, modified, and then need to be passed back to the caller.