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  2. Inverse trigonometric functions - Wikipedia

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

    The most common convention is to name inverse trigonometric functions using an arc- prefix: arcsin(x), arccos(x), arctan(x), etc. [1] (This convention is used throughout this article.) This notation arises from the following geometric relationships: [ citation needed ] when measuring in radians, an angle of θ radians will correspond to an arc ...

  3. atan2 - Wikipedia

    en.wikipedia.org/wiki/Atan2

    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.

  4. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Thus, in settings beyond elementary geometry, radians are regarded as the mathematically natural unit for describing angle measures. 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 ...

  5. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    provided the angle is measured in radians. Angles measured in degrees must first be converted to radians by multiplying them by ⁠ / ⁠. These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science.

  6. List of trigonometric identities - Wikipedia

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

    5 Power-reduction formulae. 6 Product-to-sum and sum-to-product identities. ... [12] Arctangent ⁡ ⁡ = ⁡ [13] Arccotangent ⁡ ⁡ = ⁡ Sines and cosines of ...

  7. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    As discussed in § Constructibility, only certain angles that are rational multiples of radians have trigonometric values that can be expressed with square roots. The angle 1°, being π / 180 = π / ( 2 2 ⋅ 3 2 ⋅ 5 ) {\displaystyle \pi /180=\pi /(2^{2}\cdot 3^{2}\cdot 5)} radians, has a repeated factor of 3 in the denominator and therefore ...

  8. List of common coordinate transformations - Wikipedia

    en.wikipedia.org/wiki/List_of_common_coordinate...

    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 :

  9. Magic angle - Wikipedia

    en.wikipedia.org/wiki/Magic_angle

    Magic angle. The magic angle θ m is = ⁡ = ⁡ , where arccos and arctan are the inverse cosine and tangent functions respectively. OEIS: A195696. θ m is the angle between the space diagonal of a cube and any of its three connecting edges, see image.