Trigonometry/Trigonometric Formula Reference

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Exercise: Remembering Formulae

Cover the right hand side of each formula, and use the information about remembering formulae from the previous page to get the right hand side.

Principal Trig Relationships[edit | edit source]

The following identities give relationships between the trigonometric functions.

Pythagoras related[edit | edit source]

Worked Example: The cot formula is missing

One formula is missing.

By dividing the by

or by

we can get two other formulae.

The missing formula is obtained by dividing through by

The missing formula is:

Periodicity[edit | edit source]

Four trigonometric functions are periodic:

Two trigonometric functions are periodic:

Angle Sums[edit | edit source]

Formulae involving sums of angles are as follows:

Multiple Angle Formulae[edit | edit source]

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.

Trigonometric functions of some closely related angles[edit | edit source]

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 | edit source]

cos(x)[edit | edit source]

tan(x)[edit | edit source]

Exercise: Radians

Rewrite the above formulas using radians.