the following terminology: is the solar azimuth angle is the solar zenith angle is the hour angle, in the local solar time is the current sun declination 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. The formula based on the subsolar point and the atan2 function A 2021 publication presents a method that uses a solar azimuth formula based on the subsolar point and the atan2 function, as defined in Fortran 90, that gives an unambiguous solution without the need for circumstantial treatment. The subsolar point is the point on the surface of the Earth where the Sun is overhead. The method first calculates the declination of the Sun and equation of time using equations from The Astronomical Almanac, then it gives the x-, y- and z-components of the unit vector pointing toward the Sun, through vector analysis rather than spherical trigonometry, as follows: where is the declination of the Sun, is the latitude of the subsolar point, is the longitude of the subsolar point, is the Greenwich Mean Time or UTC, is the equation of time in minutes, is the latitude of the observer, is the longitude of the observer, are the x-, y- and z-components, respectively, of the unit vector pointing toward the Sun. It can be shown that . With the above mathematical setup, the solar zenith angle and solar azimuth angle are simply , . (South-Clockwise Convention) where is the solar zenith angle, is the solar azimuth angle following the South-Clockwise Convention. If one prefers North-Clockwise Convention, or East-Counterclockwise Convention, the formulas are , (North-Clockwise Convention) . (East-Counterclockwise Convention) Finally, the values of , and at 1-hour step for an entire year can be presented in a 3D plot of "wreath of analemmas" as a graphic depiction of all possible positions of the Sun in terms of solar zenith angle and solar azimuth angle for any given location. Refer to sun path for similar plots for other locations. See also Equation of time Horizontal coordinate system Hour angle Position of the Sun Solar time Solar tracker Sun path Sunrise Sunset Zenith References External links Solar Position Calculators by National Renewable Energy Laboratory (NREL) Solar Position Algorithm for Solar Radiation Applications (NREL) An Excel workbook with VBA functions for solar azimuth, solar elevation, dawn, sunrise, solar noon,