Trigonometric Functions of Compound Angles

1. Trigonometric Functions of Compound Angles

2. Compound Angle Formulae

3. Compound Angle Formulae (A) Sum and Difference Formulae

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

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

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

8. From the quotient relation and the above formulae,

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

11. Exercise 7.1 P.235

14. Exercise 7.2 P.244

15. The Subsidiary Angles

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.

17. Exercise 7.3 P.251

18. Sums and Products of Trigonometric Functions

20. +)

21. -)

22. +)

23. -)

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

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

30. Exercise 7.4 P.257

31. Elimination of Angles

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.

33. Identities to be used in this section.

34. General Solutions of Trigonometric Equations

35. Inverse Trigonometric Functions

36. Inverse Trigonometric Functions

37. Inverse Trigonometric Functions

38. General Solutions

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

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

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

42. Exercise 7.5 P.267