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# Trigo Ratios

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### Trigo Ratios

1. 1. I would like to give credit to the following people below for the wonderful PowerPoint presentation. Thank you very much, Ms. Garcia Moy Yee Ping 3 Szeto Kwok Fai 2 Chau Ping 1
2. 2. Trigonometry ( 三角幾何 ) means “ Triangle” and “Measurement” Introduction Trigonometric Ratios
3. 3. Adjacent , Opposite Side and Hypotenuse of a Right Angle Triangle .
4. 4. Adjacent side Opposite side hypotenuse 
5. 5. hypotenuse Adjacent side Opposite side 
6. 6. Three Types Trigonometric Ratios <ul><li>There are 3 kinds of trigonometric ratios we will learn. </li></ul><ul><ul><li>sine ratio </li></ul></ul><ul><ul><li>cosine ratio </li></ul></ul><ul><ul><li>tangent ratio </li></ul></ul>
7. 7. Sine Ratios <ul><li>Definition of Sine Ratio. </li></ul><ul><li>Application of Sine Ratio. </li></ul>
8. 8. <ul><li>Definition of Sine Ratio . </li></ul>1 If the hypotenuse equals to 1 Sin  =  Opposite sides
9. 9. <ul><li>Definition of Sine Ratio . </li></ul>For any right-angled triangle Sin  =  Opposite side hypotenuses
10. 10. Exercise 1 In the figure, find sin  Sin  = Opposite Side hypotenuses = 4 7  = 34.85  (corr to 2 d.p.)  4 7
11. 11. Exercise 2 11 In the figure, find y Sin35  = Opposite Side hypotenuses y 11 y = 6.31 (corr to 2.d.p.) 35 ° y Sin35  = y = 11 sin35 
12. 12. Cosine Ratios <ul><li>Definition of Cosine. </li></ul><ul><li>Relation of Cosine to the sides of right angle triangle. </li></ul>
13. 13. <ul><li>Definition of Cosine Ratio . </li></ul>1 If the hypotenuse equals to 1 Cos  =  Adjacent Side
14. 14. <ul><li>Definition of Cosine Ratio . </li></ul>For any right-angled triangle Cos  =  hypotenuses Adjacent Side
15. 15. Exercise 3  3 8 In the figure, find cos  cos  = adjacent Side hypotenuses = 3 8  = 67.98  (corr to 2 d.p.)
16. 16. Exercise 4 6 In the figure, find x Cos 42  = Adjacent Side hypotenuses 6 x x = 8.07 (corr to 2.d.p.) 42 ° x Cos 42  = x = 6 Cos 42 
17. 17. Tangent Ratios <ul><li>Definition of Tangent. </li></ul><ul><li>Relation of Tangent to the sides of right angle triangle. </li></ul>
18. 18. <ul><li>Definition of Tangent Ratio. </li></ul>For any right-angled triangle tan  =  Adjacent Side Opposite Side
19. 19. Exercise 5  3 5 In the figure, find tan  tan  = adjacent Side Opposite side = 3 5  = 78.69  (corr to 2 d.p.)
20. 20. Exercise 6 z 5 In the figure, find z tan 22  = adjacent Side Opposite side 5 z z = 12.38 (corr to 2 d.p.) 22  tan 22  = 5 tan 22  z =
21. 21. Conclusion Make Sure that the triangle is right-angled
22. 22. The END