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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.
For a complete list of antiderivative functions, see Lists of integrals. For the special antiderivatives involving trigonometric functions, see Trigonometric integral. [1] Generally, if the function is any trigonometric function, and is its derivative,
Liouville's theorem (differential algebra) – Says when antiderivatives of elementary functions can be expressed as elementary functions; List of limits; List of mathematical identities; List of mathematical series; Nonelementary integral – Integrals not expressible in closed-form from elementary functions
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
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.}
The six trigonometric functions are defined for every real number, except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°). Referring to the diagram at the right, the six trigonometric functions of θ are, for angles smaller than the right angle:
4 Trigonometric functions. 5 Rational functions. 6 Exponential function. 7 Numeric series. ... This list of mathematical series contains formulae for finite and ...
The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions. For a complete list of integral formulas, see lists of integrals. The inverse trigonometric functions are also known as the "arc functions".