Question

What are the components of the vector between the origin and the polar coordinate `(2, pi/6)`?

Answer 1

See explanation.

Explanation:

If the polar coordinates of P are `(r, theta)` and O is the origin, the

Cartesian coordinates of P are `(x, y) = (rcostheta, rsintheta)`.

If `veci and vecj` are unit vectors in the directions Ox and Oy, then

`vec(OP) = xveci+yvecj=(rcostheta)veci+(rsintheta)vecj`.

Conveniently, this is presented in the component-coordinate form as

`vec(OP) = < x, y> = < rcostheta, rsintheta> or r < costheta, sintheta>`