I'm reviewing solar geometry calculations regarding to shading problems and, in the basic case, one wants to know whether a point will be shaded by another point at certain distance, height, azimuth angle made by both points regardint the N-S line and date.
The problem essentially reduces to calculate the solar zenith angle for that specified day when the solar azimuth angle is equal to the azimuth angle made by the points and compare it to the altitude angle made by both points (if the altitude angle is greater than the zenith angle, the point is shaded).
My issue is that equations in literature calculate the zenith first according to location and datetime, and then the solar azimuth as a function of the zenith. Both are correlated, but trying to solve the equations as functions of the solar azimuth seems to be analytically intractable (online equation solvers don't give answers).
I either want to know whether is a equation of the zenith as a function of the solar azimuth or if there is an analytical solution for the equation:
a sin(x) + b cos(x) = c
I tried solving the solar azimuth equation as a function of the zenith, and ran into a equation of the basic form a sin(x) + b cos(x) = c, which apparently has no analytical answer.
