Question

Express the polar coordinates (-3, pi/2) as Cartesian coordinates.

Answer 1

$\bf x=rcos(\theta )\qquad \qquad y=rsin(\theta )\\\\ -------------------------------\\\\ \begin{array}{cllcll} (-3&,&\frac{\pi }{2})\\ \uparrow &&\uparrow \\ r&&\theta \end{array}\implies \begin{cases} x=-3cos\left( \frac{\pi }{2} \right)\\ \qquad -3\cdot 0\\ \qquad 0\\ -----\\ y=-3sin\left( \frac{\pi }{2} \right)\\ \qquad -3\cdot 1\\ \qquad -3 \end{cases}\implies (0,-3)$