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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 nontrigonometric 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 Multipleangle formulae
6.1 Double, triple, and halfangle
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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View Full Document 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 Powerreduction formula
8 Producttosum and sumtoproduct
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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This note was uploaded on 03/01/2012 for the course EE 101 taught by Professor Munk during the Spring '12 term at Alaska Anch.
 Spring '12
 MUNK

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