Question

What are the components of the vector between the origin and the polar coordinate `(-8, (5pi)/3)`?

Answer 1

`-4i +4sqrt3 j`

Explanation:

In cartesian coordinates `x= rcos theta`. In this case it would be `x=-8 cos ((5pi)/3)= -8cos (-pi/3)= -4` and `y= r sin theta= -8 sin((5pi)/3)= -8 sin (-pi/3)= 4sqrt3`. The point would lie in 2nd quadrant.

Its vector form would be `-4i +4sqrt3 j`