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  2. 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.

  3. Inverse trigonometric functions - Wikipedia

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

    The notations sin −1 (x), cos −1 (x), tan1 (x), etc., as introduced by John Herschel in 1813, [7] [8] are often used as well in English-language sources, [1] much more than the also established sin [−1] (x), cos [−1] (x), tan [−1] (x) – conventions consistent with the notation of an inverse function, that is useful (for example ...

  4. Proofs of trigonometric identities - Wikipedia

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

    1.5.3 Tangent and cotangent. 1.6 Double-angle identities. 1.7 Half-angle identities. ... 2.5 Proof of compositions of trig and inverse trig functions. 3 See also. 4 ...

  5. 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.

  6. Inverse tangent integral - Wikipedia

    en.wikipedia.org/wiki/Inverse_tangent_integral

    The inverse tangent integral is related to the Legendre chi function = + + + by: [1] Ti 2 ⁡ ( x ) = − i χ 2 ( i x ) {\displaystyle \operatorname {Ti} _{2}(x)=-i\chi _{2}(ix)} Note that χ 2 ( x ) {\displaystyle \chi _{2}(x)} can be expressed as ∫ 0 x artanh ⁡ t t d t {\textstyle \int _{0}^{x}{\frac {\operatorname {artanh} t}{t}}\,dt ...

  7. Category:Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Category:Inverse...

    Inverse secant; Inverse sine; Inverse tangent; Inverse vercosine; Inverse versine This page was ... This page was last edited on 5 March 2020, at 10:32 (UTC).

  8. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    In the integral , we may use = ⁡, = ⁡, = ⁡. Then, = ⁡ ⁡ = ⁡ (⁡) = ⁡ ⁡ = = + = ⁡ +. The above step requires that > and ⁡ > We can choose to be the principal root of , and impose the restriction / < < / by using the inverse sine function.

  9. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [ 1 ] In the table below, the label "Undefined" represents a ratio 1 : 0. {\displaystyle 1:0.}