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Summary Of: Cosine

Cosine takes an angle and tells the run... just multiply the sine and cosine by the radius... The sine and cosine functions graphed on the Cartesian plane... The sine and cosine functions graphed on the Cartesian plane... The sine and cosine functions graphed on the Cartesian plane... only sine and cosine were defined directly by the unit circle... of sine is cosine and the derivative of cosine is the negative of sine... that the sine and cosine functions are the... Both the sine and cosine functions satisfy the... and the cosine function is the unique solution satisfying the initial conditions... Since the sine and cosine functions are linearly independent... This method of defining the sine and cosine functions is essentially equivalent to using Euler... used not only to define the sine and cosine functions but also to prove the... If an argument to sine or cosine in radians is scaled by frequency... of the sine plus the square of the cosine is always 1... which give the sine and cosine of the sum and difference of two angles in terms of sines and cosines of... cosine and tangent of any integer multiple of... cosine and tangent of an angle of... And can also be used to find the cosine of an angle... The sine and cosine functions are one... sum of sine and cosine functions of different frequencies...

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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 | Derivatives 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 | 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 | 2007 | 09-08 | 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 "Cosine".