# Trigonometry/Trigonometric Formula Reference

## Contents

Exercise: Remembering Formulas
Cover the right hand side of each formula, and use the information about remembering formulas from the previous page to get the right hand side. |

## Principal Trig Relationships[edit]

The following identities give relationships between the trigonometric functions.

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Worked Example: The cot formula is missing
One formula is missing. By dividing the by or by we can get two other formulas. The missing formula is obtained by dividing through by The missing formula is: |

### Periodicity[edit]

Four trigonometric functions are periodic:

Two trigonometric functions are periodic:

### Angle Sums[edit]

Formulas involving sums of angles are as follows:

### Multiple Angle Formulas[edit]

Substituting gives the **double angle formulae**

Substituting gives

These can be obtained by putting in the addition formula.

This can also be obtained from the angle sums formula.

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This list may duplicate some of the periodicity formulas above, but all the formulas are given for the sake of completeness. Angles are expressed in degrees rather than radians. Similar relations for cot, sec and cosec follow immediately from the definitions of these functions; just replace sin by cosec, cos by sec and tan by cot (and vice versa).

### sin(x)[edit]

### cos(x)[edit]

### tan(x)[edit]

Exercise: Radians
Rewrite the above formulas using radians. |