1. Reciprocal Trig Ratios Objectives: To learn and calculate secant, cosecant and cotangent in degrees and radians. To derive and recognise the graphs of sec, cosec and cot. To derive Pythagorean identities. Exact values pairs

2. Reciprocal Trig Ratios SUMMARY Also, The 3 reciprocal ratios are:

3. Reciprocal Trig Ratios x x x The domain is The range is x is not any multiple of  ,,

4. Reciprocal Trig Ratios The domain is The range is ,, Substitute a few values of n to convince yourself this is correct! We get Asymptote

5. Reciprocal Trig Ratios The domain is The range is The graph of can be found by using as we did for. ,, 

6. Reciprocal Trig Ratios e.g. Solve the equation for Solution: Multiply by : We may meet the reciprocal functions in an equation. Reciprocal ratios solving

7. Reciprocal Trig Ratios Principal values: We need exact answers in radians but remember we can use our calculators in degrees and then convert to radians using So, either we can write down directly from memory: or from the calculator: To find the other solutions, I use a graph. If, in doing AS, you used a different method and you are happy with it, stick to it. You can still check your answers from my graphs.

8. Reciprocal Trig Ratios for So,

9. Reciprocal Trig Ratios for Outside interval So, Add 2  to

10. Reciprocal Trig Ratios Bingo In pairs or 3s

20. Exact values pairs

21. Trig Identities Using Reciprocal Ratios There are 2 identities involving the reciprocal ratios which we will prove. We start with the identity we met in AS Dividing by : But, and So, handout

22. Trig Identities Using Reciprocal Ratios There are 2 identities involving the reciprocal ratios which we will prove. We start with the identity we met in AS Dividing by : But, and So,

23. Trig Identities Using Reciprocal Ratios There are 2 identities involving the reciprocal ratios which we will prove. We start with the identity we met in AS Dividing by : So, But, and

24. Trig Identities Using Reciprocal Ratios There are 2 identities involving the reciprocal ratios which we will prove. We start with the identity we met in AS Dividing by : So, But, and

25. Trig Identities Using Reciprocal Ratios There are 2 identities involving the reciprocal ratios which we will prove. We start with the identity we met in AS Dividing by : So, But, and

26. Trig Identities Using Reciprocal Ratios Exercise Starting with find an identity linking and Solution: Dividing by : But, and So,

27. Trig Identities Using Reciprocal Ratios SUMMARY There are 3 quadratic trig identities: Never try to square root these identities.

28. Trig Identities Using Reciprocal Ratios The trig identities are used in 2 ways: to solve some quadratic trig equations to prove other identities

29. Trig Equations Using Reciprocal Ratios To find the reciprocal, flip over the fraction e.g. 1 Solve the equation for the interval giving answers correct to the nearest degree. Solution: If isn’t on your calculator use Brackets !

30. Trig Equations Using Reciprocal Ratios e.g. 1 Solve the equation for the interval giving answers correct to the nearest degree. Solution: If isn’t on your calculator use

31. Trig Equations Using Reciprocal Ratios To solve we don’t need a graph: we just keep adding to the principal solution. So,

32. Trig Equations Using Reciprocal Ratios Exercise Solve the following equations in the intervals given 1. 2.

33. Trig Equations Using Reciprocal Ratios Solutions: 1.

34. Trig Equations Using Reciprocal Ratios Principal values: Ans:

35. Trig Equations Using Reciprocal Ratios Principal values: Ans:

36. Trig Equations Using Reciprocal Ratios Principal value: 2. ( No solutions )

37. Trig Equations Using Reciprocal Ratios Ans: Principal value:

38. Trig Equations Using Reciprocal Ratios Exam Questions

39. Trig Equations Using Reciprocal Ratios

41. 3tan 2 x = 17 – 11 sec x

42. Trig Equations Using Reciprocal Ratios More on mathsnet

43. Reciprocal Trig Ratios SUMMARY Also, The 3 reciprocal ratios are:

44. Reciprocal Trig Ratios

46. e.g. Solve the equation for Solution: Multiply by : We may meet the reciprocal functions in an equation.

47. Reciprocal Trig Ratios Principal values: We need exact answers in radians but remember we can use our calculators in degrees and then convert to radians using So, either we can write down directly from memory: or from the calculator: To find the other solutions, I use a graph. If, in doing AS, you used a different method and you are happy with it, stick to it. You can still check your answers from my graphs.

48. Reciprocal Trig Ratios for Outside interval So, Add 2  to

49. Reciprocal Trig Ratios SUMMARY There are 3 quadratic trig identities: Never try to square root these identities.

50. Reciprocal Trig Ratios e.g. 1 Solve the equation for the interval giving answers correct to the nearest degree. Solution: If isn’t on your calculator use

51. Reciprocal Trig Ratios To solve we don’t need a graph: we just keep adding to the principal solution. So,