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Trigonometry identities
All these identities can be derived from first principles. But there are a lot of them and some are hard to remember.
Print this page as a handy quick reference guide.
Recall that these identities work both ways. That is,
if you have an expression that matches the left or right side of an identity,
you can replace it with the thing on the other side.
Reciprocal identities
Ratio identities
| 1. |  |
| 2. |  |
Opposite Angle identities
| 1. |  | |
| 2. |  |
Caution - not like the other two! |
| 3. |  | |
Pythagorean identities
Complementary angle identities
* Note:
is 90° in radians. If A is in degrees, use 90 instead of
.
For example sinA = cos(90 – A)
The sum identities
The difference identities
The double angle identities
The half angle identities
The sine identities
These show how to represent the sine function in terms of the other five functions.
Some of these identities may also appear under other headings.
The cosine identities
These show how to represent the cosine function in terms of the other five functions.
Some of these identities may also appear under other headings.
The tangent identities
These show how to represent the tangent function in terms of the other five functions.
Some of these identities may also appear under other headings.
The cosecant identities
These show how to represent the cosecant function in terms of the other five functions.
Some of these identities may also appear under other headings.
The secant identities
These show how to represent the secant function in terms of the other five functions.
Some of these identities may also appear under other headings.
The cotangent identities
These show how to represent the cotangent function in terms of the other five functions.
Some of these identities may also appear under other headings.
(C) 2009 Copyright Math Open Reference. All rights reserved
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