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Drill 3/15/12

a. Drill 3/15/12. c. Name a ratio equal to if the triangles are similar: . f. e. c. b. a. d. Objective. STW learn the vocabulary relating angles to sides in right triangles for trigonometry STW explore the sine and cosine ratios, and two of the properties associated with them.

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Drill 3/15/12

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  1. a Drill 3/15/12 c • Name a ratio equal to if the triangles are similar: f e c b a d

  2. Objective • STW learn the vocabulary relating angles to sides in right triangles for trigonometry • STW explore the sine and cosine ratios, and two of the properties associated with them.

  3. Objective • SW explore the sine and cosine ratios, and two of the properties associated with them.

  4. Right Triangle

  5. Greek Letters • angle theta 

  6. Side Names in relation to  • hypotenuse 

  7. Side Names in relation to  • Adjacent side (means next to) 

  8. Side Names in relation to  • Opposite side (means across from) 

  9. Classify the Side:

  10. Classify the Side:

  11. Classify the Side:

  12. Abbreviations: hypotenuse (hyp.) opposite (opp.)  Adjacent (adj.)

  13. Tangent Ratios: • Tangent ratio of = opp./adj. opp. (alpha)  adj.

  14. Abbreviation: • Tan = opp./adj. opp.  adj.

  15. Abbreviation: • Find Tan = 3  5

  16. Abbreviation: • Find Tan A= 7 A 2

  17. Abbreviation: B • Find Tan B= 7 2

  18. Abbreviation: • Find Tan =  5 3

  19. Abbreviation: • Find Tan =  b a

  20. Calculator: • Find Tan =, if =35 

  21. Calculator: • Change to degree mode • Hit tan 35

  22. Calculator: • Hit tan 35 • Tan 35 ≈ 0.7

  23. Inverse Tangent: • If Tan =opp/adj, then the inverse tangent, abbreviated tan-1(also referred to as arctan)is used to find the angle, when given the sides

  24. Abbreviation: • Find : • tan =5/3 • tan-1 (tan )= • =tan-1(5/3)=?  3 tan-1(5/3) 5

  25. Use a calculator: • =tan-1(5/3)=? • Hit 2nd tan (5/3) • =59.04 You must use degree mode!!

  26. Sine Ratios: • Sine ratio of = opp./hyp. hyp. opp. 

  27. Abbreviation: • Sin = opp./hyp. hyp. opp. 

  28. Finding Sine Ratios: • sin  = ?  7 5

  29. Cosine Ratios: • Cosine ratio of = adj./hyp. hyp.  adj.

  30. Abbreviation: • Cos = adj./hyp. hyp.  adj.

  31. Finding Cosine Ratios: • cos = ?  7 5

  32. Calculator: • Find sin  and cos , if =35 

  33. Calculator: • Change to degree mode • Hit sin 35

  34. Calculator: • Hit sin 35 • sin 35 ≈ 0.57

  35. Calculator: • Change to degree mode • Hit cos 35

  36. Calculator: • Hit cos 35 • cos 35 ≈ 0.82

  37. Inverse sine and cosine: • If sin =opp/hyp and cos =adj/hyp, then the inverse sin and cos, abbreviated sin-1 and cos-1(also referred to as arcsin and arccos)is used to find the angle, when given the sides

  38. CW/HW • Example Ex 11-1 # 1-12 and • Example Ex All

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