Question

What are the components of the vector between the origin and the polar coordinate `(25, (-pi)/6)`?

Answer 1

In practice, this question simply asks for the coordinates to be converted from polar to rectangular (Cartesian) coordinates, since the components of the vector will be the `x` and `y` distances. In this case, `(21.7, -12.5)`.

Explanation:

The components of the vector are simply the `x` and `y` coordinates of the point at its tip. We are given the polar coordinates of that point but need the rectangular coordinates:

`x=rcostheta = 25 cos (-pi/6) = 25*0.866 = 21.7`

`t=rsintheta = 25 sin (-pi/6) = 25*(-0.5) = -12.5`

That means the coordinates of the point at the tip of the vector are `(21.7, -12.5)`.