Question

Find the rectangular coordinates of the point with the polar coordinates (3,3/2_ )

Answer 1

Polar coordinates: $(r,\theta)$

$r=3,\theta= \frac{3\pi}{2}$

Rectangular coordinates: $(x,y)=(r \cos{\theta},r \sin{\theta})$

$x=r \cos{\theta}=3 \cos{ \frac{3\pi}{2} }=3 \times 0=0 \\ y=r \sin{\theta}=3 \sin{ \frac{3\pi}{2} }=3 \times (-1)=-3$

Rectangular coordinates are (0,-3).