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In geometry, the polar angle may be 2D polar angle, the angular coordinate of a two-dimensional polar coordinate system; 3D polar angle, ...
Even with these restrictions, if the polar angle (inclination) is 0° or 180°—elevation is −90° or +90°—then the azimuth angle is arbitrary; and if r is zero, both azimuth and polar angles are arbitrary. To define the coordinates as unique, the user can assert the convention that (in these cases) the arbitrary coordinates are set to zero.
the point's direction from the pole relative to the direction of the polar axis, a ray drawn from the pole. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1] The pole is analogous to the origin in a Cartesian coordinate system.
The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by φ ∈ [ 0 , 2 π ] {\displaystyle \varphi \in [0,2\pi ]} : it is the angle between the x -axis and the projection of the radial vector onto the xy -plane.
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 system) is called the pole, and the ray from the pole in the reference direction is the polar axis.
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by an angle and a distance.The polar coordinate system is especially useful in situations where the relationship between two points is most easily expressed in terms of angles and distance; in the more familiar Cartesian or rectangular coordinate system, such a ...
In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. [1] In geography, Southern latitudes are defined to be negative, and as a result the colatitude is a non-negative quantity, ranging from zero at the North pole to 180° at the South pole.
The cosine rule may be used to give the angles A, B, and C but, to avoid ambiguities, the half angle formulae are preferred. Case 2: two sides and an included angle given (SAS). The cosine rule gives a and then we are back to Case 1. Case 3: two sides and an opposite angle given (SSA). The sine rule gives C and then we have Case 7. There are ...