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Summary Of: Trigonometric function

The first step in computing any trigonometric function is range reduction...

Encyclodia Page On: Trigonometric function

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Sine (disambiguation) | mathematics | functions | angle | study | triangles | periodic phenomena | ratios | unit circle | infinite series | differential equations | complex numbers | Trigonometry | History | Usage | Inverse functions | Further reading | List of identities | Exact constants | Generating trigonometric tables | CORDIC | Euclidean | Law of sines | Law of cosines | Law of tangents | Pythagorean theorem | Calculus | Trigonometric integral | Trigonometric substitution | Integrals of functions | Integrals of inverses | History of trigonometric functions | Identities | radians | similar triangles | Hipparchus | Nicaea | Ptolemy | Egypt | Aryabhata | Varahamihira | Brahmagupta | Muḥammad ibn Mūsā al-Ḵwārizmī | Abū al-Wafā' al-Būzjānī | Omar Khayyam | Bhāskara II | Nasir al-Din al-Tusi | Ghiyath al-Kashi | Ulugh Beg | Regiomontanus | Rheticus | Valentin Otho | citation needed | Madhava of Sangamagramma | analysis | infinite series | citation needed | Leonhard Euler | Euler's formula | chord | versine | haversine | exsecant | excosecant | trigonometric identities | Etymologically | Sanskrit | transliterated | Arabic | 12th century | Latin | A right triangle always includes a 90° (π/2 radians) angle, here labeled C. Angles A and B may vary. Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle. | | right triangle | The sine, tangent, and secant functions of an angle constructed geometrically in terms of a unit circle. The number θ is the length of the curve; thus angles are being measured in radians. The secant and tangent functions rely on a fixed vertical line and the sine function on a moving vertical line. ("Fixed" in this context means not moving as θ changes; "moving" means depending on θ.) Thus, as θ goes from 0 up to a right angle, sin θ goes from 0 to 1, tan θ goes from 0 to ∞, and sec θ goes from 1 to ∞. | | radians | The cosine, cotangent, and cosecant functions of an angle θ constructed geometrically in terms of a unit circle. The functions whose names have the prefix co- use horizontal lines where the others use vertical lines. | | right triangle | hypotenuse | Euclidean plane | radians | ° | ° | unit circle | periodic functions | similar | multiplicative inverse | multiplicative inverse | multiplicative inverse | slope | unit circle | The unit circle | | unit circle | unit circle | circle | Pythagorean theorem | The sine and cosine functions graphed on the Cartesian plane. | | Trigonometric functions: Sine, Cosine, Tangent, Cosecant, Secant, Cotangent | | periodic functions | integer | asymptote | All of the trigonometric functions of the angle θ can be constructed geometrically in terms of a unit circle centered at O. | | India | citation needed | versin | tangent | secant lines | exsec | citation needed | The sine function (blue) is closely approximated by its Taylor polynomial of degree 7 (pink) for a full cycle centered on the origin. | | Taylor polynomial | limits | derivative | calculus | radians | Taylor series | real numbers | citation needed | Fourier series | infinite series | real number system | differentiability | continuity | up/down number | Bernoulli number | Euler number | combinatorial | alternating permutations | citation needed | combinatorial | alternating permutations | citation needed | complex analysis | analytic continuation | imaginary | complex exponential function | Euler's formula | complex plane | | | | | | | differential equation | function space | basis | linear differential equation | trigonometric identities | eigenfunctions | List of trigonometric identities | Pythagorean theorem | Ptolemy | product-to-sum identities | logarithm function | integrals | derivatives | table of derivatives | table of integrals | list of integrals of trigonometric functions | mathematical analysis | functional equations | real functions | citation needed | trigonometry in Galois fields | computers | scientific calculators | Generating trigonometric tables | interpolating | significant figures | identities | floating point | polynomial | rational | approximation | Chebyshev approximation | Padé approximation | Taylor | Laurent series | table lookup | hardware multipliers | CORDIC | shifts | hardware | floating point units | arithmetic-geometric mean | complex | elliptic integral | Exact trigonometric constants | Pythagorean theorem | radians | exactly by hand | Inverse trigonometric functions | injective | inverse function | bijective | arcsecond | Inverse trigonometric function | complex logarithm | Uses of trigonometry | trigonometry | law of sines | triangle | circumcircle | A Lissajous curve, a figure formed with a trigonometry-based function. | | Lissajous curve | triangulation | law of cosines | Pythagorean theorem | Pythagorean theorem | SSA ambiguous case | law of tangents | Animation of the additive synthesis of a square wave with an increasing number of harmonics | | square wave | simple harmonic motion | uniform circular motion | periodic functions | waves | Fourier analysis | square wave | Fourier series | Generating trigonometric tables | Hyperbolic function | Pythagorean theorem | Unit vector | Table of Newtonian series | List of trigonometric identities | Proofs of trigonometric identities | Euler's formula | Polar sine | All Students Take Calculus | Continued fraction of Gauss | continued fraction | Euler's_formula#Using Taylor series | Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables | ISBN 0-486-61272-4 | Boyer, Carl B. | ISBN 0-471-54397-7 | Penguin Books | ISBN 0-691-00659-8 | ISBN 0-691-09541-8 | ISBN 0-19-853446-9 | MacTutor History of Mathematics Archive | MacTutor History of Mathematics Archive | MacTutor History of Mathematics Archive | MathWorld | 21 January | 2006 | Wikibooks | Wikibooks | Categories | Trigonometry | Elementary special functions | Transcendental numbers | All articles with unsourced statements | Articles with unsourced statements since June 2008 | Articles with unsourced statements since March 2008 |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Trigonometric function".