the sign (since the hour angle is positive westward instead of east). In cartography The cartographical azimuth or grid azimuth (in decimal degrees) can be calculated when the coordinates of 2 points are known in a flat plane (cartographical coordinates): Remark that the reference axes are swapped relative to the (counterclockwise) mathematical polar coordinate system and that the azimuth is clockwise relative to the north. This is the reason why the X and Y axis in the above formula are swapped. If the azimuth becomes negative, one can always add 360°. The formula in radians would be slightly easier: Note the swapped in contrast to the normal atan2 input order. The opposite problem occurs when the coordinates (X1, Y1) of one point, the distance D, and the azimuth α to another point (X2, Y2) are known, one can calculate its coordinates: This is typically used in triangulation and azimuth identification (AzID), especially in radar applications. Map projections There is a wide variety of azimuthal map projections. They all have the property that directions (the azimuths) from a central point are preserved. Some navigation systems use south as the reference plane. However, any direction can serve as the plane of reference, as long as it is clearly defined for everyone using that system. Related coordinates Right ascension If, instead of measuring from and along the horizon, the angles are measured from and along the celestial equator, the angles are called right ascension if referenced to the Vernal Equinox, or hour angle if referenced to the celestial meridian. Polar coordinate In mathematics, the azimuth angle of a point in cylindrical coordinates or spherical coordinates is the anticlockwise angle between the positive x-axis and the projection of the vector onto the xy-plane. The angle is the same as an angle in polar coordinates of the component of the vector in the xy-plane and is normally measured in radians rather than degrees. As well as measuring the angle differently, in mathematical applications theta, θ, is very often used to represent the azimuth rather than the representation of symbol phi φ. Other uses For magnetic tape drives, azimuth refers to the angle between the tape head(s) and tape. In sound localization experiments and literature, the azimuth refers to the angle the sound source makes compared to the imaginary straight line that is drawn from within the head through the area between the eyes. An azimuth