Question

What are the components of the vector between the origin and the polar coordinate `(-5, (3pi)/2)`?

Answer 1

The vertical y-component is `5` and there is no horizontal x-component.

Explanation:

For a polar co-ordinate `(r,theta`), we may find the rectangular components `(x,y)` from the transformations :\

`x=rcostheta and y=rsintheta`.

`therefore x=-5cos((3pi)/2)=0`

`y=-5sin((3pi)/2)=5`

Thus the rectangular form is `(0,5)`.