Question

What are the components of the vector between the origin and the polar coordinate `(6, pi/3)`?

Answer 1

`(3,3sqrt(3))`

Explanation:

The coordinates of the vector are the rectangular coordinates.

So let's convert the polar coordinates to rectangular form using the formula:

`(r, theta)->(x,y)`

`x=rcostheta`
`y=rsintheta`

`x=(6)cos(pi/3)=6(1/2)=3`

`y=(6)sin(pi/3)=6(sqrt(3)/2)=3sqrt(3)`

So the vector components are `(3, 3sqrt(3))`