Question

What are the components of the vector between the origin and the polar coordinate `(5, (23pi)/12)`?

Answer 1

Rectangular coordinates `color(green)((4.8296, -1.2941)`

Explanation:

To find the Cartesian coordinates, given the polar coordinates.

`(r, theta) => (5, (23pi)/12)`

`x = r cos theta = 5 cos ((23pi)/12) = 4.8296`

`y = r sin theta = 5 * sin ((23pi)/12) = -1.2941`

`tan theta = tan ((23pi)/12) = -0.2679`