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Graph of over. In computing and mathematics, the function atan2 is the 2- argument arctangent. By definition, is the angle measure (in radians, with ) between the positive -axis and the ray from the origin to the point in the Cartesian plane. Equivalently, is the argument (also called phase or angle) of the complex number (The argument of a ...
In blue, the point (4, 210°). In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ...
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three real numbers: the radial distance r along the radial line connecting the point to the fixed point of origin; the polar angle θ between the radial line and a given polar axis; [a ...
e. In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [1] cyclometric, [2] or arcus functions [3]) are the inverse functions of the trigonometric functions, under suitably restricted domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions ...
As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range of 180°, running from 0° to 180°, and does not pose any problem when calculated from an arccosine, but beware for an arctangent. If, in the alternative definition, θ is chosen to run from − ...
As with the Mercator projection, the region near the tangent (or secant) point on a Stereographic map remains very close to true scale for an angular distance of a few degrees. In the ellipsoidal model, a stereographic projection tangent to the pole has a scale factor of less than 1.003 at 84° latitude and 1.008 at 80° latitude.
However, the above geometry may be used to give an independent proof of the sine rule. The scalar triple product, OA → · (OB → × OC →) evaluates to sin b sin c sin A in the basis shown. Similarly, in a basis oriented with the z-axis along OB →, the triple product OB → · (OC → × OA →), evaluates to sin c sin a sin B.
Sunrise equation. A contour plot of the hours of daylight as a function of latitude and day of the year, using the most accurate models described in this article. It can be seen that the area of constant day and constant night reach up to the polar circles (here labeled "Anta. c." and "Arct. c."), which is a consequence of the earth's inclination.