"Logarithmic sine" redirects here. For the Clausen-related function, see log sine function.
"Logarithmic cosine" redirects here. For the Clausen-related function, see log cosine function.
Trigonometry
Outline
History
Usage
Functions (sin, cos, tan, inverse)
Generalized trigonometry
Reference
Identities
Exact constants
Tables
Unit circle
Laws and theorems
Sines
Cosines
Tangents
Cotangents
Pythagorean theorem
Calculus
Trigonometric substitution
Integrals (inverse functions)
Derivatives
Trigonometric series
Mathematicians
Hipparchus
Ptolemy
Brahmagupta
al-Hasib
al-Battani
Regiomontanus
Viète
de Moivre
Euler
Fourier
v
t
e
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][2] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions.
The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend the sine and cosine functions to functions whose domain is the whole real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used; then the domain of the other functions is the real line with some isolated points removed. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane with some isolated points removed.
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and 28 Related for: Trigonometric functions information
mathematics, the trigonometricfunctions (also called circular functions, angle functions or goniometric functions) are real functions which relate an...
and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometricfunctions are widely used...
In mathematics, sine and cosine are trigonometricfunctions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle:...
tables of values for trigonometric ratios (also called trigonometricfunctions) such as sine. Throughout history, trigonometry has been applied in areas...
The differentiation of trigonometricfunctions is the mathematical process of finding the derivative of a trigonometricfunction, or its rate of change...
In trigonometry, trigonometric identities are equalities that involve trigonometricfunctions and are true for every value of the occurring variables for...
Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometricfunctions began in Hellenistic mathematics...
functions. For a complete list of antiderivative functions, see Lists of integrals. For the special antiderivatives involving trigonometricfunctions...
The trigonometricfunctions (especially sine and cosine) for real or complex square matrices occur in solutions of second-order systems of differential...
application of trigonometric tables and generation schemes is for fast Fourier transform (FFT) algorithms, where the same trigonometricfunction values (called...
periodic function into a sum of trigonometricfunctions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are...
There are several equivalent ways for defining trigonometricfunctions, and the proofs of the trigonometric identities between them depend on the chosen...
functions produce meaningful values for any real-valued angle measure – even those greater than 2π. In fact, all six standard trigonometricfunctions –...
In mathematics, hyperbolic functions are analogues of the ordinary trigonometricfunctions, but defined using the hyperbola rather than the circle. Just...
the inverse trigonometricfunctions. For a complete list of integral formulas, see lists of integrals. The inverse trigonometricfunctions are also known...
the function chosen to be dv. An alternative to this rule is the ILATE rule, where inverse trigonometricfunctions come before logarithmic functions. To...
theorem TrigonometricfunctionTrigonometry of a tetrahedron Triangle (also see List of triangle topics) Sine, Cosine, Tangent (trigonometricfunction), Cotangent...
In trigonometry, it is common to use mnemonics to help remember trigonometric identities and the relationships between the various trigonometric functions...
to the trigonometricfunctions. Inverse hyperbolic functions: inverses of the hyperbolic functions, analogous to the inverse circular functions. Logarithms:...
In mathematics, the values of the trigonometricfunctions can be expressed approximately, as in cos ( π / 4 ) ≈ 0.707 {\displaystyle \cos(\pi /4)\approx...
polynomials, exponential function ex, and the trigonometricfunctions sine and cosine, are examples of entire functions. Examples of functions that are not entire...
Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions...
versine or versed sine is a trigonometricfunction found in some of the earliest (Sanskrit Aryabhatia, Section I) trigonometric tables. The versine of an...
In mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometricfunctions. The different sine integral definitions...
word of دالة زائدية "hyperbolic function") is added to the end of trigonometricfunctions to express hyperbolic functions. This is similar to the way h...
In mathematics, a trigonometric substitution replaces a trigonometricfunction for another expression. In calculus, trigonometric substitutions are a...
Polar/Trigonometric forms of hypercomplex numbers Polygonometry – trigonometric identities for multiple distinct angles The Lemniscate elliptic functions,...
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