## Precalculus (6th Edition) Blitzer

multiplying, $r$, $x^2+y^2$, $y$
Please note that according to the definition of the trigonometric functions and by applying the Pythagorean theorem, we have the following relations between polar and rectangular coordinates:$$x=r\cos \theta, \qquad y=r\sin \theta, \\ r^2=x^2+y^2, \qquad \tan \theta =\frac{y}{x}.$$ Thus, the answers are: multiplying, $r$, $x^2+y^2$, $y$