Question

Which set of rectangular coordinates describes the same location as the polar coordinates (4,3pi/2)?

Answer 1

\[\begin{cases}x=r\cos\theta\\
y=r\sin\theta\end{cases}~~\iff~~\begin{cases}x=4\cos\dfrac{3\pi}{2}\\\\
y=4\sin\dfrac{3\pi}{2}\end{cases}~~\iff~~\begin{cases}x=0\\\\
y=-4\end{cases}\]