Answer
(a) $(\frac{3\sqrt 2}{2},-\frac{3\sqrt 2}{2})$
(b) $(0,-4)$
Work Step by Step
(a) Given the polar coordinates $(3,315^\circ)$, we have $x=r\ cos\theta =3cos315^\circ=\frac{3\sqrt 2}{2}, y=r\ sin\theta = 3sin315^\circ=-\frac{3\sqrt 2}{2}$, that is $(\frac{3\sqrt 2}{2},-\frac{3\sqrt 2}{2})$
(b) Given the polar coordinates $(-4,90^\circ)$, we have $x=r\ cos\theta =-4cos90^\circ=0, y=r\ sin\theta = -4sin90^\circ=-4$, that is $(0,-4)$
