Question

What are the components of the vector between the origin and the polar coordinate `(8, (pi)/6)`?

Answer 1

Component of the vector along `x` axis is `4sqrt3` and component along `y` axis is `4`.

Explanation:

Components of a vector between the origin and the polar coordinate `(r, theta)` are `r cos theta` (along `x` axis)
and `r sin theta` (along `y` axis).

Accordingly components are `8 cos pi/6` (along `x` axis)
and `8 sin pi/6` (along `y` axis).

As `cos pi/6 = sqrt 3/2` and `sin pi/6 = 1/2`,

component of the vector along `x` axis is `8* sqrt 3/2` or `4sqrt3` and component along `y` axis is `8* 1/2` or `4`.