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The concept of the position angle is inherited from nautical navigation on the oceans, where the optimum compass course is the course from a known position s to a target position t with minimum effort. Setting aside the influence of winds and ocean currents, the optimum course is the course of smallest distance between the two positions on the ...
A rotation through angle θ with non-standard axes. If a standard right-handed Cartesian coordinate system is used, with the x-axis to the right and the y-axis up, the rotation R(θ) is counterclockwise. If a left-handed Cartesian coordinate system is used, with x directed to the right but y directed down, R(θ) is clockwise.
The azimuth angle (or longitude) of a given position on Earth, commonly denoted by λ, is measured in degrees east or west from some conventional reference meridian (most commonly the IERS Reference Meridian); thus its domain (or range) is −180° ≤ λ ≤ 180° and a given reading is typically designated "East" or "West".
A polar grid with several angles, increasing in counterclockwise orientation and labelled in degrees. The radial coordinate is often denoted by r or ρ, and the angular coordinate by φ, θ, or t. The angular coordinate is specified as φ by ISO standard 31-11. However, in mathematical literature the angle is often denoted by θ instead.
Figure 2: A rotation represented by an Euler axis and angle. In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of the Euler's rotation theorem ; the magnitude specifies the rotation in radians about that axis (using the right-hand ...
When Cartesian coordinates are represented by standard position, defined by the x-axis rightward and the y-axis upward, positive rotations are anticlockwise, and negative cycles are clockwise. In many contexts, an angle of −θ is effectively equivalent to an angle of "one full turn minus θ". For example, an orientation represented as −45 ...
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents the distance in relation to an arbitrary reference origin O , and its direction represents the angular orientation with respect to given reference axes.
Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere.