The document provides information about trigonometric ratios including sine, cosine, and tangent ratios. It gives examples of using each ratio to calculate lengths and angles in right triangles. It also provides mixed problems examples that require using more than one ratio to solve.

1. The Sin e Ratio The Cos ine Ratio Mixed Problems The Tan gent Ratio

2. Starter Questions www.mathsrevision.com www.mathsrevision.com S4

3. 16 Feb 2010 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 2. Use sine ratio to find a length or angle. Define the sine ratio and show how to find a length or angle using this ratio. Trigonometry 1. Write down sine ratio. Sine ratio S4

4. The Sine Ratio x° Sin x ° = Opposite Opp Hyp hypotenuse S4

5. 34° Sin x ° = Opp Opp Hyp Hyp h 11cm Sin 34 ° = h 11 = h 11 x Sin 34 ° h = 11 x Sin 34 ° = 6.2cm (1 d.p.) Find the height h S O H C A H T O A Sine Ratio S4

6. x° Sin x ° = Opp Opp Hyp Hyp 6m 9m Sin x ° = 6 9 = 0.667 (3 d.p.) Sin x ° Find the x o S O H C A H T O A Sine Ratio S4

7. How do we find x °? 2 nd Sin ⁻ ¹ is written above To get this press Sin Followed by Sine Ratio =0.667 (3 d.p.) Sin x ° We need to use Sin ⁻ ¹ on the calculator. Sin Sin ⁻ ¹

8. x = Sin ⁻ ¹ 0.667 = 41.8 ° (1 d.p.) 2 nd Press Enter = 0.667 Sine Ratio = 0.667 (3 d.p.) Sin x ° Sin Sin ⁻ ¹

9. S O H C A H T O A 16 Feb 2010 Compiled by Mr. Lafferty Maths Dept. The support rope is 11.7m long. The angle between the rope and ground is 70 o . Use the sine ratio to calculate the height of the flag pole. 11.7m Sine Ratio 70 o h

10. S O H C A H T O A 16 Feb 2010 Compiled by Mr. Lafferty Maths Dept. Use the sine ratio to find the angle of the ramp. 20 m Sine Ratio x o 10m

11. S O H C A H T O A 72° Sin x ° = Opp Hyp Sin 72 ° = 5 r r = r = 5.3 km 5km A B C r A road AB is right angled at B. The road BC is 5 km. Calculate the length of the new road AC. Sine Ratio S4

12. Now try Ex 1 & 2 Ch 13 Page 148 Sine Ratio S4

13. Starter Questions www.mathsrevision.com www.mathsrevision.com S4

14. 16 Feb 2010 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 2. Use cosine ratio to find a length or angle. Definite the cosine ratio and show how to find an length or angle using this ratio. Trigonometry 1. Write down cosine ratio. Cosine Ratio S4

15. Cos x ° = Adjacent Adj x° Hyp hypotenuse Cosine Ratio S4

16. S O H C A H T O A 40° Cos x ° = Opp Adj Hyp Hyp b 35mm Cos 40 ° = b 35 = b 35 x Cos 40 ° b = 35 x Cos 40 ° = 26.8mm (1 d.p.) Adj Find the adjacent length b Cosine Ratio S4

17. S O H C A H T O A x° Cos x ° = Opp Adj Hyp Hyp 45cm Cos x ° = 34 45 = 0.756 (3 d.p.) Cos x ° x = Cos ⁻ ¹0.756 =41 ° Adj 34cm S4 Find the angle x o Cosine Ratio

18. Now try Ex 3 Ch 13 Page 153 Cosine Ratio S4

19. Starter Questions www.mathsrevision.com www.mathsrevision.com S4

20. 16 Feb 2010 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 2. Use tan of an angle to solve problems. To use tan of the angle to solve problems. Angles & Triangles 1. Write down tan ratio.

21. 12 m How high is the tower? 60 ° Opp

22. 60 ° 12 m Adjacent Opposite hypotenuse Copy this!

23. Tan x ° = Opp Adj Tan 60 ° = Opp 12 = Opp 12 x Tan 60 ° Opp = 12 x Tan 60 ° = 20.8m (1 d.p.) Copy this!

24. So the tower’s 20.8 m high! Don’t worry, you’ll be trying plenty of examples!! 20.8m

25. Adj x° Tan x ° = Opposite Opp Adjacent S4 General

26. Example 65° Tan x ° = Opp Opp Adj Hyp h 8m Tan 65 ° = h 8 = h 8 x Tan 65 ° h = 8 x Tan 65 ° = 17.2m (1 d.p.) Adj S4 General Find the height h S O H C A H T O A

27. Extension Booklet

28. Past Paper Type Questions S O H C A H T O A Mixed Ratios S4

29. The Three Ratios www.mathsrevision.com Cosine Sine Tangent Sine Sine Tangent Cosine Cosine Sine www.mathsrevision.com opposite opposite opposite adjacent adjacent adjacent hypotenuse hypotenuse hypotenuse S4

30. C A H T O A S O H Mixed Ratios S4 Sin x ° = O pp H yp Cos x ° = A dj H yp Tan x ° = O pp A dj

31. S O H C A H T O A 1. Write down Process Identify what you want to find what you know 3. 2. Mixed Ratios S4 Copy this!

32. Past Paper Type Questions (4 marks) S O H C A H T O A Mixed Ratios S4

33. Past Paper Type Questions S O H C A H T O A Mixed Ratios S4

34. Past Paper Type Questions S O H C A H T O A 4 marks Mixed Ratios S4

35. Past Paper Type Questions S4 S O H C A H T O A Mixed Ratios

36. Past Paper Type Questions S4 (4marks) S O H C A H T O A Mixed Ratios

37. Past Paper Type Questions S4 S O H C A H T O A Mixed Ratios

38. Past Paper Type Questions S4 (4marks) S O H C A H T O A Mixed Ratios

39. Now try Ex 4 Ch 13 Page 157 Mixed Ratios S4