Question

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

Choices:
(-3,0)
(-3,3)
(0,-3)
(3,-3)

Answer 1

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