Editing Solar azimuth angle (section)

==Conventional Trigonometric Formulas==
The following formulas assume the north-clockwise convention. The solar azimuth angle can be calculated to a good approximation with the following formula, however angles should be interpreted with care because the [[inverse sine]], i.e. {{math|1=''x'' = sin<sup>−1</sup> y}} or {{math|1=''x'' = arcsin ''y''}}, has multiple solutions, only one of which will be correct.
:<math>\sin \phi_\mathrm{s} = \frac{-\sin h \cos \delta}{\sin \theta_\mathrm{s}}.</math>

The following formulas can also be used to approximate the solar azimuth angle, but these formulas use cosine, so the azimuth angle as shown by a calculator will always be positive, and should be interpreted as the angle between zero and 180 degrees when the hour angle, {{mvar|h}}, is negative (morning) and the angle between 180 and 360 degrees when the hour angle, {{mvar|h}}, is positive (afternoon). (These two formulas are equivalent if one assumes the "[[solar elevation angle]]" approximation formula).<ref name="Seinfeld and Pandis" /><ref name="Duffie" /><ref name="SPA" />

:<math>\begin{align}
   \cos \phi_\mathrm{s} &= \frac{\sin \delta \cos \Phi - \cos h \cos \delta \sin \Phi}{\sin \theta_\mathrm{s}} \\[5pt]
   \cos \phi_\mathrm{s} &= \frac{\sin \delta - \cos \theta_\mathrm{s}\sin \Phi}{\sin \theta_\mathrm{s}\cos \Phi}.
 \end{align}</math>

So practically speaking, the compass azimuth which is the practical value used everywhere (in example in airlines as the so called course) on a compass (where North is 0 degrees, East is 90 degrees, South is 180 degrees and West is 270 degrees) can be calculated as 

:<math>\text{compass } \phi_\mathrm{s} = 360 - \phi_\mathrm{s}.</math>

The formulas use the following terminology:
*<math>\phi_\mathrm{s}</math> is the solar azimuth angle
*<math>\theta_\mathrm{s}</math> is the [[solar zenith angle]]
*<math>h</math> is the [[hour angle]], in the local [[solar time]]
*<math>\delta</math> is the current [[Position of the Sun|sun declination]]
*<math>\Phi</math> is the local [[latitude]]

In addition, dividing the above sine formula by the first cosine formula gives one the tangent formula as is used in ''The Nautical Almanac''.<ref>The Nautical Almanac https://thenauticalalmanac.com/Formulas.html</ref>