express 20sin theta + 4 cos theta as R sin(theta + alpha)

Question

R sin(theta + alpha) =
R cos(alpha)sin(theta) +
R sin(alpha)cos(theta)

---->

Rcos(alpha) = 20

Rsin(alpha) = 4

The x-y coordinates of a point on a circle of radius R that makes an angle og alpha with the positive x-axis are with radius R are R cos(alpha) and R sin(alpha) respectively.

R follows from:

20^2 + 4^2 = R^2

If you divide the two equations you get tan(alpha)