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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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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


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)


Exercise 7.1

P.235


Exercise 7.2

P.244


The Subsidiary Angles


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.


Exercise 7.3

P.251


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.


Exercise 7.4

P.257


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 of Trigonometric Equations


Inverse Trigonometric Functions


Inverse Trigonometric Functions


Inverse Trigonometric Functions


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.


Exercise 7.5

P.267


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