Solar azimuth angle

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The solar azimuth angle is the azimuth angle of the sun. It is most often defined as the angle between the line from the observer to the sun projected on the ground and the line from the observer due south. A positive azimuth angle generally indicates the sun is east of south, and a negative azimuth angle generally indicates the sun is west of south. Others define solar azimuth as the angle from due north in a clockwise direction.

It can be calculated, to a good approximation, using the following formula, however angles should be interpreted with care due to the inverse sine. For example: x = sin^-1(y) has more than one solution, therefore at a northern latitude in summer, when the azimuth at sunrise should be a positive number greater than 90 degrees, inverse of sine will incorrectly yield an angle between 0 and 90 degrees that has the same sine.

$\, \sin \phi_\mathrm{s} = \frac{-\sin h \cos \delta}{\cos \theta_\mathrm{s}}$

The following two formulas can also be used to approximate the solar azimuth angle, however because these formulas utilize cosine, the azimuth angle will always be positive, and therefore, should be interpreted as the angle east of south when the hour angle, h, is negative (morning) and the angle west of south when the hour angle, h, is positive (afternoon).

$\, \cos \phi_\mathrm{s} = \frac{\cos h \cos \delta \sin \Phi - \sin \delta \cos \Phi} {\cos \theta_\mathrm{s}}$