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Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are 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 system is based on two foci F 1 and F 2. Referring to the figure at right, the σ-coordinate of a point P equals the angle F 1 P F 2, and the τ-coordinate equals the natural logarithm of the ratio of the distances d 1 and d 2: = .
In the cylindrical coordinate system, a z-coordinate with the same meaning as in Cartesian coordinates is added to the r and θ polar coordinates giving a triple (r, θ, z). [8] Spherical coordinates take this a step further by converting the pair of cylindrical coordinates ( r , z ) to polar coordinates ( ρ , φ ) giving a triple ( ρ , θ ...
In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes sin ( 30 ∘ ) = 1 / 2 {\displaystyle \sin(30^{\circ ...
The most common definition of toroidal coordinates (,,) is = = = together with () = ().The coordinate of a point equals the angle and the coordinate equals the natural logarithm of the ratio of the distances and to opposite sides of the focal ring
When this is not the case, as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be written using decimal degrees (DD notation); for example, 40.1875°. Alternatively, the traditional sexagesimal unit subdivisions can be used: one degree is divided into 60 minutes (of arc) , and one minute into 60 ...