Slide 1 Trigonometric Functions of Compound Angles

Slide 2 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 Slide 14 Slide 15 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 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 Slide 31 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 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