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  2. List of integrals of trigonometric functions - Wikipedia

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

    For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals. For the special antiderivatives involving trigonometric functions, see Trigonometric integral. [1]

  3. List of integrals of hyperbolic functions - Wikipedia

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

    3.1 Integrals of hyperbolic tangent, cotangent, secant, cosecant functions 3.2 Integrals involving hyperbolic sine and cosine functions 3.3 Integrals involving hyperbolic and trigonometric functions

  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 integral - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_integral

    2 Cosine integral. 3 Hyperbolic sine ... is the antiderivative of sin x / x whose value is zero at x = 0, ... are accurate to better than 10 −16 for 0 ≤ x ≤ 4, ...

  6. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    Leonhard Euler used it to evaluate the integral / (+ ⁡) in his 1768 integral calculus textbook, [3] and Adrien-Marie Legendre described the general method in 1817. [ 4 ] The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [ 5 ]

  7. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    3.1 Integrals with a singularity. 3.2 Rational functions. 3.3 Exponential functions. ... dx is an antiderivative of f on every interval on which f is not zero, ...

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  9. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.

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