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atan2(y, x) returns the angle θ between the positive x-axis and the ray from the origin to the point (x, y), confined to (−π, π].Graph of (,) over /. In computing and mathematics, the function atan2 is the 2-argument arctangent.
[1] [10] Another precarious convention used by a small number of authors is to use an uppercase first letter, along with a “ −1 ” superscript: Sin −1 (x), Cos −1 (x), Tan −1 (x), etc. [11] Although it is intended to avoid confusion with the reciprocal, which should be represented by sin −1 (x), cos −1 (x), etc., or, better, by ...
Note that the arctan functions implemented in computer languages only produce results between −π/2 and π/2, which is why atan2 is used to generate all the correct orientations. Moreover, typical implementations of arctan also might have some numerical disadvantages near zero and one. Some implementations use the equivalent expression: [3]
The atan2 function should be used to determine σ 01, λ, and α. For example, to find the midpoint of the path, substitute σ = 1 ⁄ 2 (σ 01 + σ 02); alternatively to find the point a distance d from the starting point, take σ = σ 01 + d/R.
When programming these equations, the inverse tangent function used is actually the atan2 function, with the first argument sin φ and the second cos φ cos λ. The reverse operation is composed of the operations:
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Looking at the sources, the Mathworld one doesn't actually use atan2, the Cazelais source is a broken link, and I can't verify the Apostol source but it's unlikely that it uses atan2. (It's dated 1967, while atan2 was first introduced to Fortran in 1961, and I doubt the terminology moved into a standard calculus text that early.)
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