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Trigonometric Functions of Compound Angles


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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Trigonometric functions of compound angles l.jpg

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


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Exercise 7.2

P.244


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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


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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.


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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.


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Exercise 7.5

P.267