The calculator finds \( R \) using \( R = \sqrt{x^2 + y^2} \). Then finds the quadrant using the signs of \( x \) and \( y \) and solves any of the equations:
\[
x = R \cos \theta \quad \text{or} \quad y = R \sin \theta
\]
for \( \theta \) such that \( \theta\) is in the range \( (-\pi, \pi] \) or in degrees \( (-180^\circ, 180^\circ] \).