# Trigonometry (trig) identities

All these trig 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 whatever is on the other side.

## A. Reciprocal identities

## B. Ratio identities

## C. Opposite Angle identities

## D. Pythagorean identities

## E. Complementary angle identities

* Note:
is 90° in radians.

If A is in degrees, use 90 instead of

For example:

## F. Supplementary angle identities

This basically says that if two angles are supplementary (add to 180°) they have the same sine.

## G. The sum identities

## H. The difference identities

## J. The double angle identities

## K. The half angle identities

## M. 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.

## N. 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.

## P. The tangent identities

These show how to represent the tangent function in terms of the other five functions.
Some of these trig identities may also appear under other headings.

## Q. The cosecant identities

These show how to represent the cosecant function in terms of the other five functions.
Some of these trig identities may also appear under other headings.

## R. The secant identities

These show how to represent the secant function in terms of the other five functions.
Some of these trig identities may also appear under other headings.

## S. 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.

## Linking to this page

If you would like to make links to this page, you can customize the link so it points to a particular identity or group of identities.
The link should be the URL of the page, followed by a #, follwed by the section or identity you want. For example

```
mathopenref.com/trigidentities.html
```

Will link to the top of this page

```
mathopenref.com/trigidentities.html#c
```

Will link to this page with the page scrolled so that Section C is at the top

```
mathopenref.com/trigidentities.html#h2
```

Will link to this page with the page scrolled so that the identity h2 is at the top and outlined.

For example
mathopenref.com/trigidentities.html#h2

(C) 2011 Copyright Math Open Reference.

All rights reserved