Spam protection caused a duplicate of this post. Closing this one. https://gamedev.net/forums/topic/714968-calculating-the-far-distance-plan-based-on-pitch-and-yaw-for-a-map-renderer/

A rotation matrix is used. It's simple and it's standard.

By the way, whenever you have two real numbers that are the cosine and the sine of a number, you can think of them as a single complex number, z = cos(a)+i*sin(a) == exp(i*a) == polar(1,a). You can then recover the angle by computing a = atan2(imag(z),real(z)) == real(-i*log(z)) == arg(z).