# relative azimuth angle derivations

1. relative azimuth angle from sensor and solar azimuth angle

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(\varphi_{0}\) | solar azimuth angle | \(deg\) | solar_azimuth_angle {:}
   \(\varphi_{r}\) | relative azimuth angle | \(deg\) | relative_azimuth_angle {:}
   \(\varphi_{S}\) | sensor azimuth angle | \(deg\) | sensor_azimuth_angle {:}

   The pattern : for the dimensions can represent {time}, or no dimensions at all.

   \begin{eqnarray} \Delta\varphi & = & \varphi_{0} - \varphi_{S} \\ \Delta\varphi & = & \begin{cases} \Delta\varphi \geq 360, & \Delta\varphi - 360 \\ 0 \leq \Delta\varphi < 360, & \Delta\varphi \\ \Delta\varphi < 0, & \Delta\varphi + 360 \end{cases} \\ \varphi_{r} & = & \left|\Delta\varphi - 180 \right| \end{eqnarray}