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A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to 1 / 60 of one degree. [1] Since one degree is 1 / 360 of a turn, or complete rotation , one arcminute is 1 / 21 600 of a turn.
This computation produces a different result than the arithmetic mean, with the difference being greater when the angles are widely distributed. For example, the arithmetic mean of the three angles 0°, 0°, and 90° is (0° + 0° + 90°) / 3 = 30°, but the vector mean is arctan(1/2) = 26.565°.
If = then is 45 degrees or radians. This means that if the real part and complex part are equal then the arctangent will equal π 4 {\textstyle {\frac {\pi }{4}}} . Since the arctangent of one has a very slow convergence rate if we find two complex numbers that when multiplied will result in the same real and imaginary part we will have a ...
L 1, L 2: longitude of the points; L = L 2 − L 1: difference in longitude of two points; λ: Difference in longitude of the points on the auxiliary sphere; α 1, α 2: forward azimuths at the points; α: forward azimuth of the geodesic at the equator, if it were extended that far; s: ellipsoidal distance between the two points; σ: angular ...
Machin's formula [4] (for which the derivation is straightforward) is: = The benefit of the new formula, a variation on the Gregory–Leibniz series ( π / 4 = arctan 1), was that it had a significantly increased rate of convergence, which made it a much more practical method of calculation.
When radians (rad) are employed, the angle is given as the length of the arc of the unit circle subtended by it: the angle that subtends an arc of length 1 on the unit circle is 1 rad (≈ 57.3°), and a complete turn (360°) is an angle of 2 π (≈ 6.28) rad.
The angle is typically measured in degrees from the mark of number 12 clockwise. The time is usually based on a 12-hour clock. A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute.
arctan(1.0) to arctan(10) ... ρ, ρ 0 or 1° 0.0175: π/180: radians per degree: R: 57.29: 180/π: degrees per radian: ρ' 3.438x10 3: 60x180/π: arc minutes per ...