# solar azimuth angle derivations

1. solar azimuth angle from latitude and solar declination/hour/zenith angles

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(\theta_{0}\) | solar zenith angle | \(deg\) | solar_zenith_angle {time}
   \(\delta\) | solar declination angle | \(deg\) | solar_declination_angle {time}
   \(\phi\) | latitude | \(degN\) | latitude {time}
   \(\varphi_{0}\) | solar azimuth angle | \(deg\) | solar_azimuth_angle {time}
   \(\omega\) | solar hour angle | \(deg\) | solar_hour_angle {time}

   \begin{eqnarray} \varphi_{0} & = & \begin{cases} \sin(\frac{\pi}{180}\theta_{0}) = 0, & 0 \\ \sin(\frac{\pi}{180}\theta_{0}) \neq 0 \wedge \omega > 0, & -\frac{180}{\pi}\arccos(\frac{\sin(\frac{\pi}{180}\delta)\cos(\frac{\pi}{180}\phi) - \cos(\frac{\pi}{180}\omega)\cos(\frac{\pi}{180}\delta)\sin(\frac{\pi}{180}\phi)}{\sin(\frac{\pi}{180}\theta_{0})}) \\ \sin(\frac{\pi}{180}\theta_{0}) \neq 0 \wedge \omega <= 0, & \frac{180}{\pi}\arccos(\frac{\sin(\frac{\pi}{180}\delta)\cos(\frac{\pi}{180}\phi) - \cos(\frac{\pi}{180}\omega)\cos(\frac{\pi}{180}\delta)\sin(\frac{\pi}{180}\phi)}{\sin(\frac{\pi}{180}\theta_{0})}) \end{cases} \end{eqnarray}