Chapter 10.2, Problem 1QCE

(a) Rectangular coordinates of a point $\left(x,y\right)$ may be recovered from its polar coordinates $\left(r,\theta \right)$ by means of the equations $x=\text{\_\_\_\_\_ and }y=\text{\_\_\_\_\_}\text{.}$

(b) Polar coordinates $\left(r,\theta \right)$ may be recovered from rectangular coordinates $\left(x,y\right)$ by means of the equations $r^2=\text{\_\_\_\_\_ and }\tan \theta =\text{\_\_\_\_\_}\text{.}$