how to convert rectangular coordinates to polar coordinates

To convert rectangular coordinates (x,y)(x,y)(x,y) to polar coordinates (r,θ)(r,\theta)(r,θ), you:

• Compute the radius: r=x2+y2r=\sqrt{x^{2}+y^{2}}r=x2+y2​.

• Compute the angle: θ=arctan⁡ ⁣(yx)\theta =\arctan\!\left(\dfrac{y}{x}\right)θ=arctan(xy​), then adjust θ\theta θ to the correct quadrant based on the signs of xxx and yyy (often using a two-argument arctangent like atan2 in calculators or software).

That’s the entire conversion in a nutshell.