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Trigonometric Functions of Compound Angles






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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.
Trigonometric Functions of Compound Angles

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Trigonometric functions of compound angles l.jpgSlide 1

Trigonometric Functions of Compound Angles

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Compound Angle Formulae

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Compound Angle Formulae

(A) Sum and Difference Formulae

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

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

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

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From the quotient relation and the above formulae,

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

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Exercise 7.1

P.235

Exercise 7 2 l.jpgSlide 14

Exercise 7.2

P.244

The subsidiary angles l.jpgSlide 15

The Subsidiary Angles

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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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Exercise 7.3

P.251

Sums and products of trigonometric functions l.jpgSlide 18

Sums and Products of Trigonometric Functions

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+)

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-)

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+)

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-)

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

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

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Exercise 7.4

P.257

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Elimination of Angles

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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.

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Identities to be used in this section.

General solutions of trigonometric equations l.jpgSlide 34

General Solutions of Trigonometric Equations

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Inverse Trigonometric Functions

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Inverse Trigonometric Functions

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Inverse Trigonometric Functions

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General Solutions

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

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

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

Exercise 7 5 l.jpgSlide 42

Exercise 7.5

P.267


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