# Difference between revisions of "Trigonometric identities"

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− | Trigonometric identities are used to manipulate trig equations in certain ways. Here is a list of them: | + | '''Trigonometric identities''' are used to manipulate trig equations in certain ways. Here is a list of them: |

+ | == Basic Definitions == | ||

+ | The six basic trigonometric functions can be defined using a right triangle: | ||

− | == Reciprocal | + | <center>[[Image:righttriangle.png]]</center> |

+ | |||

+ | The six trig functions are sine, cosine, tangent, cosecant, secant, and cotangent. They are abbreviated by using the first three letters of their name (except for cosecant which uses <math>\csc</math>). They are defined as follows: | ||

+ | |||

+ | {| style="width:75%; height:200px; margin: 1em auto 1em auto" border="0" | ||

+ | |- | ||

+ | | <math>\sin A = \frac ac</math> || <math>\csc A = \frac ca</math> | ||

+ | |- | ||

+ | | <math> \cos A = \frac bc</math> || <math>\sec A = \frac cb</math> | ||

+ | |- | ||

+ | | <math> \tan A = \frac ab</math> || <math> \cot A = \frac ba</math> | ||

+ | |} | ||

+ | |||

+ | == Reciprocal Relations == | ||

+ | From the last section, it is easy to see that the following hold: | ||

+ | |||

+ | {| style="width:75%; margin: 1em auto 1em auto" | ||

+ | |- | ||

+ | | <math> \sin A = \frac 1{\csc A}</math> || <math> \cos A = \frac 1{\sec A}</math> || <math> \tan A = \frac 1{\cot A}</math> | ||

+ | |} | ||

== Pythagorean Identities == | == Pythagorean Identities == | ||

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*<math>|1-e^{i\theta}|=2\sin\frac{\theta}{2}</math> | *<math>|1-e^{i\theta}|=2\sin\frac{\theta}{2}</math> | ||

− | |||

− | |||

==See also== | ==See also== |

## Revision as of 08:34, 24 June 2006

**Trigonometric identities** are used to manipulate trig equations in certain ways. Here is a list of them:

## Contents

## Basic Definitions

The six basic trigonometric functions can be defined using a right triangle:

The six trig functions are sine, cosine, tangent, cosecant, secant, and cotangent. They are abbreviated by using the first three letters of their name (except for cosecant which uses ). They are defined as follows:

## Reciprocal Relations

From the last section, it is easy to see that the following hold:

## Pythagorean Identities

## Angle Addition Identities

## Even-Odd Identities

## Prosthaphaersis Indentities

(Otherwise known as sum-to-product identities)

## Other Identities

## See also

*This article is a stub. Help us out by expanding it.*