Irradiance onto a flat plate at certain orientation

Suppose I want to measure, say, sky or solar radiation incident upon a flat plate. The maximum irradiation will be achieved when the plate surface normal is parallel to the direction of irradiation (but in the opposite direction obviously). If I know what this irradiance is (in Watts/m2) how do I calculate the irradiance incident upon a plate at a certain orientation (i.e. what value between 0 and 1 do I need to multiply the maximum irradiation by)?

Given the tilt (-90deg is face down, 90deg is face up) and rotation angle of the plate I can work out the zenith and azimuth angles of radiation relative to the plate normal. I also suspect that this question is analogous to finding the projected surface area on a two dimensional image plane.

I began with something like cos(Az)*sin(Zen) but when the tilt was 90, I was getting an azimuthal dependence when I really shouldn't have been.

Can anyone help?