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.

Contents

Principal Trig RelationshipsEdit

The following identities give relationships between the trigonometric functions.

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Pythagoras relatedEdit

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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 formulae.

The missing formula is obtained by dividing through by  

 

The missing formula is:

 

PeriodicityEdit

Four trigonometric functions are   periodic:

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Two trigonometric functions are   periodic:

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Angle SumsEdit

Formulae involving sums of angles are as follows:

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Multiple Angle FormulaeEdit

Substituting   gives the double angle formulae

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Substituting   gives

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These can be obtained by putting   in the addition formula.

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This can also be obtained from the angle sums formula.

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Trigonometric functions of some closely related anglesEdit

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

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cos(x)Edit

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tan(x)Edit

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Exercise: Radians

Rewrite the above formulas using radians.