# Trigonometric Functions of Compound Angles - PowerPoint PPT Presentation

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Trigonometric Functions of Compound Angles. Compound Angle Formulae. Compound Angle Formulae. (A) Sum and Difference Formulae. If we replace B by (-B) in formula of sin(A – B), we have. If we replace A by ( /2 - A ) in the formula of sin(A - B), we have.

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Trigonometric Functions of Compound Angles

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## Compound Angle Formulae

(A) Sum and Difference Formulae

If we replace B by (-B) in formula of sin(A – B), we have

If we replace A by (/2 - A) in the formula of sin(A - B), we have

By substituting (- B) in the formula of cos(A + B), we have

From the quotient relation and the above formulae,

By substituting (-B) for B in the formula tan(A + B)

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## The Subsidiary Angles

The expression acos + bsin

may always be converted into the forms rsin( ±α) or rcos( ±β) where r is a positive constant.

α and β are called the subsidiary angles.

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## Sums and Products of Trigonometric Functions

+)

-)

+)

-)

If we put A + B = x and A – B = y, express in terms of x and y.

If we put A + B = x and A – B = y, express in terms of x and y.

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## Elimination of Angles

If we have two or more equations, each containing a certain variable, the process of finding an equation from which that variable isexcluded is called elimination.

Identities to be used in this section.

## General Solutions

where n is any integer and  is any root of cos = k.

where n is any integer and  is any root of sin = k.

where n is any integer and  is any root of tan = k.

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