Question

What are the components of the vector between the origin and the polar coordinate `(5, (13pi)/12)`?

Answer 1

`(-5 cos (pi/12), -5 sin(pi/12)) = (-4.83, -1.39)`, nearly.

Explanation:

The components of the radial vector to (r, `theta`) are`(x, y) = (r cos theta, r sin theta)`.

Here, r = 5 and `theta = - 13pi/12=pi+pi/12` (in the third quadrant)..

`cos (pi+pi/12)=-cos(pi/12) and sin (pi+pi/12)=-sin(pi/12)`.

So, the components (x, y) =`(-5 cos (pi/12), -5 sin(pi/12)) = (-4.83, -1.39)`, nearly.