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So first the equation:

AOI = cos-1 {cos(Tm) cos(Zs)+sin(Tm) sin(Zs) cos(AZs-AZm)}

Where:

AOI = solar angle of incidence (deg)

Tm = tilt angle of module (deg) (0deg is horizontal)

Zs = zenith angle of sun (deg)

AZm = azimuth angle of module (0deg = North, 90deg= East)

AZs = azimuth angle of sun (0deg= North, 90deg= East)

*Note that the -1 beside the cos means "ACOS" not "COS to the power of -1"

So my problem is that for a given sun postion (Zs, AZs), I want to know the best combination of Tm and AZm to give me the lowest possible value for AOI.

I calculate Tm based on AZm with the formula:

Tm = AZm x .5

I know that I need to substitute AZm x .5 for all the Tm’s in the original equation but I cannot seem to rearrange it to isolate AZm onto one side. I fear my lack of trig identity knowledge is what is preventing me from solving. I would appreciate any help or guidance anyone could give. Even just a hint.

Thanks!