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List_of_trigonometric_identities

List_of_trigonometric_identities - List of trigonometric...

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List of trigonometric identities From Wikipedia, the free encyclopedia In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities involving both angles and side lengths of a triangle. Only the former are covered in this article. 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. Cosines and sines around the unit circle Trigonometry History Usage Functions Generalized Inverse functions Further reading Reference Identities Exact constants Trigonometric tables Laws and theorems Law of sines Law of cosines Law of tangents Law of cotangents Pythagorean theorem Calculus Trigonometric substitution Integrals of functions Contents 1 Notation 1.1 Angles 1.2 Trigonometric functions 1.3 Inverse functions 2 Pythagorean identity 2.1 Related identities 3 Historic shorthands 4 Symmetry, shifts, and periodicity 4.1 Symmetry 4.2 Shifts and periodicity 5 Angle sum and difference identities 5.1 Matrix form 5.2 Sines and cosines of sums of infinitely many terms 5.3 Tangents of sums of finitely many terms 5.4 Secants and cosecants of sums of finitely many terms 6 Multiple-angle formulae 6.1 Double-, triple-, and half-angle formulae 6.2 Sine, cosine, and tangent of multiple angles 6.3 Chebyshev method Page 1 of 25 List of trigonometric identities - Wikipedia, the free encyclopedia 10/4/2011 http://en.wikipedia.org/wiki/List_of_trigonometric_identities
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Notation Angles This article uses Greek letters such as alpha ( α ), beta ( β ), gamma ( γ ), and theta ( θ ) to represent angles. Several different units of angle measure are widely used, including degrees, radians, and grads: 1 full circle = 360 degrees = 2 π radians = 400 grads. The following table shows the conversions for some common angles: Derivatives of functions Integrals of inverse functions 6.4 Tangent of an average 6.5 Viète's infinite product 7 Power-reduction formula 8 Product-to-sum and sum-to-product identities 8.1 Other related identities 8.2 Hermite's cotangent identity 8.3 Ptolemy's theorem 9 Linear combinations 10 Other sums of trigonometric functions 11 Certain linear fractional transformations 12 Inverse trigonometric functions 12.1 Compositions of trig and inverse trig functions 13 Relation to the complex exponential function 14 Infinite product formulae 15 Identities without variables 15.1 Computing π 15.2 A useful mnemonic for certain values of sines and cosines 15.3 Miscellany 15.4 An identity of Euclid 16 Calculus 16.1 Implications
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