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  2. Inverse trigonometric functions - Wikipedia

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

    [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), Cos1 (x), Tan −1 (x), etc. [11] Although it is intended to avoid confusion with the reciprocal, which should be represented by sin −1 (x), cos1 (x), etc., or, better, by ...

  3. Cos-1 - Wikipedia

    en.wikipedia.org/wiki/Cos-1

    Cos-1, one of two commonly used COS cell lines; cos x−1 = cos(x)−1 = −(1cos(x)) = −ver(x) or negative versine of x, the additive inverse (or negation) of an old trigonometric function; cos1 y = cos1 (y), sometimes interpreted as arccos(y) or arccosine of y, the compositional inverse of the trigonometric function cosine (see ...

  4. List of trigonometric identities - Wikipedia

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

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  5. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    The notations sin −1, cos1, etc. are often used for arcsin and arccos, etc. When this notation is used, inverse functions could be confused with multiplicative inverses. The notation with the "arc" prefix avoids such a confusion, though "arcsec" for arcsecant can be confused with "arcsecond".

  6. Arccos - Wikipedia

    en.wikipedia.org/wiki/Arccos

    arccos (trigonometry), the inverse trigonometric function of cosine; ARccOS protection, ... This page was last edited on 1 November 2023, at 01:54 (UTC).

  7. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    For the sine function, we can handle other values. If θ > π /2, then θ > 1. But sin θ ≤ 1 (because of the Pythagorean identity), so sin θ < θ. So we have ⁡ < <. For negative values of θ we have, by the symmetry of the sine function

  8. List of integrals of inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    There are three common notations for inverse trigonometric functions. The arcsine function, for instance, could be written as sin −1, asin, or, as is used on this page, arcsin. For each inverse trigonometric integration formula below there is a corresponding formula in the list of integrals of inverse hyperbolic functions.

  9. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...