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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.
calculate = (¯ , ¯ ), where atan2 is a computer function, also called the arctangent of two arguments, that returns the arctangent of the ratio of the two values given. Note that in Microsoft Excel the two arguments are reversed, so the proper syntax would be = atan2(AC*\sin(beta), BC*\sin(alpha)) .
The convention of atan2() returning values in the range [0, 2π) is so rare and obscure that I cannot find a single use of it. Elevating this alternate convention from footnote does not improve the article. The definition as originally presented is still the most straightforward initial definition of the function:
The function atan2(y, x) can be used instead of the mathematical function arctan(y/x) owing to its domain and image. The classical arctan function has an image of (−π/2, +π/2), whereas atan2 is defined to have an image of (−π, π].
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 .
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.
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(In fact, it is impossible to define a continuous mean operation on the circle.) In other words, the radius measures the concentration of the angles. Given the angles , …, a common formula of the mean using the atan2 variant of the arctangent function is