mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions...

a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions...

for evaluating integrals. In this case, an expression involving a radical function is replaced with a trigonometric one. Trigonometric identities may...

Certain substitutions can be made to integrals involving trigonometric functions, so the integral is transformed into a rational function of a complex variable...

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for...

of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions. For a complete list of integral formulas, see...

the lists of integrals: List of integrals of rational functions List of integrals of irrational functions List of integrals of trigonometric functions List...

wave Sine–Gordon equation Sinusoidal model SOH-CAH-TOA Trigonometric functions Trigonometric integral The superscript of −1 in sin − 1 {\displaystyle \sin...

trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the trigonometric functions...

mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential...

indicates how many times one number contains another Trigonometry Trigonometric functions Trigonometric identities Euler's formula Archimedes Aristarchus...

are other approaches to integrating trigonometric functions. For example, it can be helpful to rewrite trigonometric functions in terms of eix and e−ix...

tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas...

In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any...

t){\bigr )}\,d\lambda .} This is called an expansion as a trigonometric integral, or a Fourier integral expansion. The coefficient functions a and b can be...

formula is useful for evaluating various trigonometric integrals. In particular, it can be used to evaluate the integral of the secant cubed, which, though...

_{1}^{\infty }{\frac {e^{-tz}}{t}}\,dt} to get a relation with the trigonometric integrals Si {\displaystyle \operatorname {Si} } and Ci {\displaystyle \operatorname...

include rational and exponential functions, logarithm, trigonometric functions and inverse trigonometric functions, and the operations of multiplication and...

non-rigorous method, resembling differentiation, applicable to some trigonometric functions. Madhava of Sangamagrama and the Kerala School of Astronomy...

closed under arithmetic operations, every trigonometric number is algebraic. The minimal polynomials of trigonometric numbers can be explicitly enumerated...

are polynomials, exponential functions, logarithms, trigonometric functions, inverse trigonometric functions and their combinations under composition and...

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...

representability of a function by a trigonometric series; i.e., when can a function be represented by a trigonometric series). This paper was submitted...

functions are developed. Algebraic skills are exercised with trigonometric functions and trigonometric identities. The binomial theorem, polar coordinates, parametric...

latter manner is commonly used in trigonometric substitution, replacing the original variable with a trigonometric function of a new variable and the...

improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral. In the context...

Logarithmic integral function: Integral of the reciprocal of the logarithm, important in the prime number theorem. Exponential integral Trigonometric integral: Including...

}{\sqrt {1-k^{2}\sin ^{2}\theta }}}.} This is Legendre's trigonometric form of the elliptic integral; substituting t = sin θ and x = sin φ, one obtains Jacobi's...

of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a...

the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form...