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  2. atan2 - Wikipedia

    en.wikipedia.org/wiki/Atan2

    The two figures below show 3D views of respectively atan2(y, x) and arctan(⁠ y / x ⁠) over a region of the plane. Note that for atan2(y, x), rays in the X/Y-plane emanating from the origin have constant values, but for arctan(⁠ y / x ⁠) lines in the X/Y-plane passing through the origin have constant

  3. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    The orange sheet in the middle is the principal sheet representing arctan x. The blue sheet above and green sheet below are displaced by 2 π and −2 π respectively. Since the inverse trigonometric functions are analytic functions , they can be extended from the real line to the complex plane.

  4. Vincenty's formulae - Wikipedia

    en.wikipedia.org/wiki/Vincenty's_formulae

    U 1 = arctan( (1 − ƒ) tan Φ 1), U 2 = arctan( (1 − ƒ) tan Φ 2) reduced latitude (latitude on the auxiliary sphere) 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

  5. Trigonometric tables - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_tables

    These angles are usually arranged across the top row of the table, while the different trigonometric functions are labeled in the first column on the left. To locate the value of a specific trigonometric function at a certain angle, you would find the row for the function and follow it across to the column under the desired angle. [1]

  6. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse.

  7. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.