Question

Convert polar equation to rectangular coordinates θ = − (9π/ 2)

Answer 1

Visualize pi/2 as 90° on the unit circle. this has no real component, only imaginary. same for 3pi/2, or -pi/2 as shown in this equation:

$- \frac{ \pi}{2} = 0 - i$

as you move around the unit circle, you'll find that 9pi/2 is the same angle as pi/2.

Thus, the rectangular coordinates are:
$- \frac{9\pi}{2} = 0 - i$