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  2. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/.../Inverse_trigonometric_functions

    In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [1] cyclometric, [2] or arcus functions [3]) are the inverse functions of the trigonometric functions, under suitably restricted domains.

  3. List of trigonometric identities - Wikipedia

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

    These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

  4. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    [1] [2] Like other methods of integration by substitution, when evaluating a definite integral, ... by using the inverse sine function. ...

  5. Inverse function - Wikipedia

    en.wikipedia.org/wiki/Inverse_function

    The arcsine is a partial inverse of the sine function. These considerations are particularly important for defining the inverses of trigonometric functions. For example, the sine function is not one-to-one, since ⁡ (+) = ⁡ for every real x (and more generally sin(x + 2 π n) = sin(x) for every integer n).

  6. Proofs of trigonometric identities - Wikipedia

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

    This geometric argument relies on definitions of arc length and area, which act as assumptions, so it is rather a condition imposed in construction of trigonometric functions than a provable property. [2] 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 ...

  7. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    The names of the inverse trigonometric functions, ... These include the chord (crd(θ) = 2 sin(⁠ θ / 2 ⁠)), the versine (versin(θ) = 1 − cos(θ) = 2 sin 2 ...

  8. 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 ...

  9. Principal branch - Wikipedia

    en.wikipedia.org/wiki/Principal_branch

    A more familiar principal branch function, limited to real numbers, is that of a positive real number raised to the power of 1/2. For example, take the relation y = x 1/2, where x is any positive real number. This relation can be satisfied by any value of y equal to a square root of x (either positive or negative).