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Angle AOB is a central angle. A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). [1]
the radial distance r along the line connecting the point to a fixed point called the origin; the polar angle θ between this radial line and a given polar axis; [a] and; the azimuthal angle φ, which is the angle of rotation of the radial line around the polar axis. [b] (See graphic regarding the "physics convention".)
The point or wind, used in navigation, is 1 / 32 of a turn. 1 point = 1 / 8 of a right angle = 11.25° = 12.5 grad. Each point is subdivided into four quarter points, so one turn equals 128. milliradian: 2000π: ≈0.057°
The angle sum of a triangle is greater than 180° and less than 540°. The area of a triangle is proportional to the excess of its angle sum over 180°. Two triangles with the same angle sum are equal in area. There is an upper bound for the area of triangles.
The cotangent, or four-part, formulae relate two sides and two angles forming four consecutive parts around the triangle, for example (aCbA) or BaCb). In such a set there are inner and outer parts: for example in the set ( BaCb ) the inner angle is C , the inner side is a , the outer angle is B , the outer side is b .
A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line). Then there is a unique point on this line whose signed distance from the origin is r for given number r.
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.
If P 0 is taken to be the point (1, 1), P 1 the point (x 1, 1/x 1), and P 2 the point (x 2, 1/x 2), then the parallel condition requires that Q be the point (x 1 x 2, 1/x 1 1/x 2). It thus makes sense to define the hyperbolic angle from P 0 to an arbitrary point on the curve as a logarithmic function of the point's value of x. [1] [2]