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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.
We are given between and we know that there is an angle in some interval that satisfies =. We want to find this θ . {\displaystyle \theta .} The table above indicates that the solution is θ = ± arccos x + 2 π k for some k ∈ Z {\displaystyle \,\theta =\pm \arccos x+2\pi k\,\quad {\text{ for some }}k\in \mathbb {Z} } which is a ...
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :
Atan may refer to: Mathematics. arctangent (atan), a trigonometric function atan2, the two-argument function implementing the arctangent in many computer languages;
where atan2 is the quadrant-resolving arc-tangent function. The geocentric longitude and geodetic longitude have the same value; this is true for Earth and other similar shaped planets because they have a large amount of rotational symmetry around their spin axis (see triaxial ellipsoidal longitude for a generalization).
Styphnate, it sounds like you are describing the advantages of atan2 vs. atan. Here, it is being used instead of asin, which has no division by zero. (Actually, computers with IEEE arithmetic can divide by zero just fine and get ±∞. The advantage of atan2 over atan is more that atan2 has an expanded range, from −π to π.
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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.