In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle.
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.
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In trigonometry, trigonometricidentities are equalities that involve trigonometric functions and are true for every value of the occurring variables for...
Pythagorean trigonometricidentity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms oftrigonometric functions...
are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometricidentities between them depend on the chosen definition...
section contains the most basic ones; for more identities, see Listoftrigonometricidentities. These identities may be proved geometrically from the unit-circle...
earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied...
In trigonometry, it is common to use mnemonics to help remember trigonometricidentities and the relationships between the various trigonometric functions...
function is replaced with a trigonometric one. Trigonometricidentities may help simplify the answer. Like other methods of integration by substitution...
is a listof integrals (antiderivative functions) oftrigonometric functions. For antiderivatives involving both exponential and trigonometric functions...
differentiation oftrigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect...
Covariance Listoftrigonometricidentities Hall, Arthur Graham; Frink, Fred Goodrich (January 1909). "Chapter II. The Acute Angle [10] Functions of complementary...
application oftrigonometric tables and generation schemes is for fast Fourier transform (FFT) algorithms, where the same trigonometric function values...
Generalized trigonometry Hyperbolic function Lemniscate elliptic functions Law of sines Listof periodic functions Listoftrigonometricidentities Madhava...
by zero). For angles outside of this range, trigonometric values can be found by applying reflection and shift identities such as sin ( 2 π + θ ) = sin...
mathematical identities are relatively simple (for an experienced mathematician), though not necessarily unimportant. Trivial logarithmic identities are: By...
how many times one number contains another TrigonometryTrigonometric functions Trigonometricidentities Euler's formula Archimedes Aristarchus Aryabhata...
following is a listof indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions. For a complete listof integral...
functions Listof integrals of inverse trigonometric functions ListoftrigonometricidentitiesTrigonometric function Trigonometric functions of matrices...
a trigonometric way) that are equivalent to specific trigonometric laws or formulas. For instance, propositions twelve and thirteen of book two of the...
R sin(x−α) (see Listoftrigonometricidentities). The concept of parent function is less clear for polynomials of higher power because of the extra turning...
geometry List of trigonometry topics Outline oftrigonometryListoftrigonometricidentitiesListof logarithmic identitiesListof integrals of logarithmic...
volume Listof surface area formulas – Measure of a two-dimensional surface Listoftrigonometricidentities – Equalities that involve trigonometric functions...
derivative of the variable in question. Since (see Chain Rule and Listoftrigonometricidentities) x ˙ 1 = θ ˙ 1 ( l 2 cos θ 1 ) → x ˙ 1 2 = θ ˙ 1 2 ( l 2...
The following are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)}...
of sin(x) and cos(x), a trigonometric polynomial becomes a polynomial in the two variables sin(x) and cos(x) (using Listoftrigonometricidentities#Multiple-angle...
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