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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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Slide 1

Trigonometric Functions of Compound Angles

Slide 2

Compound Angle Formulae

Slide 3

Compound Angle Formulae

(A) Sum and Difference Formulae

Slide 5

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

Slide 6

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

Slide 7

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

Slide 8

From the quotient relation and the above formulae,

Slide 9

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

Slide 11

Exercise 7.1

P.235

Slide 14

Exercise 7.2

P.244

Slide 15

The Subsidiary Angles

Slide 16

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.

Slide 17

Exercise 7.3

P.251

Slide 18

Sums and Products of Trigonometric Functions

Slide 20

+)

Slide 21

-)

Slide 22

+)

Slide 23

-)

Slide 26

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

Slide 27

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

Slide 30

Exercise 7.4

P.257

Slide 31

Elimination of Angles

Slide 32

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.

Slide 33

Identities to be used in this section.

Slide 34

General Solutions of Trigonometric Equations

Slide 35

Inverse Trigonometric Functions

Slide 36

Inverse Trigonometric Functions

Slide 37

Inverse Trigonometric Functions

Slide 38

General Solutions

Slide 39

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

Slide 40

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

Slide 41

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

Slide 42

Exercise 7.5

P.267


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