2. TRIGONOMETRY With Tony the Triangle!!! Let’s have some fun! Click me!

3. Sine Tangent Let’s Get Started! Where to start… Click here to begin Cosine

4. SOH-CAH-TOA In Trigonometry the three basic functions that we will be learning about can be remembered by the pneumonic below: SOH-CAH-TOA Move on!

5. Directions Read through the descriptions and applications of each of the trig functions Complete the quiz at the end of each section Have your instructor come around when you have completed the quiz to gain participation points Complete the final evaluation at the end of the presentation! Click the pink triangles to continue Move on!

6. I just need to review one function SineCosineTangent I want to go through the whole presentation Let’s Go! Other Options Life Applications I’m Ready! Quiz Me!

7. The Sine Function Sine comes from the SOH part of soh-cah-toa S ine equals O pposite over H ypotenuse

8. SOH Opposite Hypotenuse Sin( )= Hypotenuse Opposite

9. Uses for the Sine Function When given a right angle triangle with an angle theta, and the length of the opposite side, the sine function can be used to compute the length of the hypotenuse of the given triangle.

10. =30 degrees Opp. Side = 1 Opposite Sin(30)= 1/hypotenuse (Hypotenuse)(Sin(30))=1 Hypotenuse = 2

11. More uses for Sine… When given a right angle triangle with the length of the hypotenuse and the length of the opposite side, the sine function can be used to compute the measure of the angle theta.

12. Hypotenuse Opposite Opp. Side = 1 Hypotenuse= sqrt(2) Sin( )= 1/sqrt(2) =45 degrees or pi/4 radians

13. And even one more use! When given a right angle triangle with an angle theta, and the length of the hypotenuse, the sine function can be used to compute the length of the opposite side of the given triangle.

14. Hypotenuse Hypotenuse= 2 =60 degrees Sin(60)= opposite side/2 2(Sin(30))=Opposite side Opposite side = 1

15. Sine Quiz Time!!! What is the value of the opposite side? = 45 degrees Hypotenuse= sqrt(2) Hypotenuse 0 1 2

16. Tony the Triangle Says… Sorry! Try again! Back to Sine

17. Tony the Triangle Says… You got it! Back to the Menu On to Cosine

18. The Cosine Function Cosine comes from the CAH part of soh-cah-toa C osine equals A djacent over H ypotenuse

19. CAH Adjacent Hypotenuse Cos( )= Hypotenuse Adjacent

20. Uses for the Cosine Function When given a right angle triangle with an angle theta, and the length of the adjacent side, the cosine function can be used to compute the length of the hypotenuse of the given triangle.

21. =30 degrees Adj. Side = sqrt(3) Adjacent Cos(30)= sqrt(3)/Hypotenuse (Hypotenuse)(Cos(30))=sqrt(3) Hypotenuse = 2

22. More uses for Cosine… When given a right angle triangle with the length of the hypotenuse and the length of the adjacent side, the cosine function can be used to compute the measure of the angle theta.

23. Hypotenuse Adj. Side = 1 Hypotenuse= sqrt(2) Cos( )= 1/sqrt(2) =45 degrees or pi/4 radians Adjacent

24. And even one more use! When given a right angle triangle with an angle theta, and the length of the hypotenuse, the cosine function can be used to compute the length of the adjacent side of the given triangle.

25. Hypotenuse Hypotenuse= 2 =60 degrees Sin(60)= Adjacent side/2 2(Sin(30))=Adjacent Side Adjacent side = 1

26. Cosine Quiz Time!!! Which variable can be found using cosine Hypotenuse y none x Theta=45 deg. Hypotenuse=sqrt(2) y x

27. Tony the Triangle Says… Get it next time! Back to Cosine

28. Tony the Triangle Says… Way to go! Back to the Menu On to Tangent

29. The Tangent Function Tangent comes from the TOA part of soh-cah-toa T angent equals O pposite over A djacent

30. TOA Adjacent Tan( )= Adjacent Opposite

31. Uses for the Tangent Function When given a right angle triangle with an angle theta, and the length of the adjacent side, the tangent function can be used to compute the length of the opposite side of the given triangle.

32. =30 degrees Adj. Side = sqrt(3) Adjacent Tan(30)= (1/sqrt(3))/Opposite (Opposite)(Tan(30))=(1/sqrt(3)) Opposite=1

33. More uses for Tangent… When given a right angle triangle with the length of the opposite side and the length of the adjacent side, the tangent function can be used to compute the measure of the angle theta.

34. Adj. Side = 1 Opposite=1 Tan( )= 1/1 =45 degrees or pi/4 radians Adjacent

35. And even one more use! When given a right angle triangle with an angle theta, and the length of the opposite side, the cosine function can be used to compute the length of the adjacent side of the given triangle.

36. Opposite= 2 =45 degrees Tan(45)= 2/(Adjacent Side) 2=(Tan(45))(Adjacent Side) Adjacent side = 2

37. Tangent Quiz Time!!! What Ratio describes the tangent function? 2/1 8/6 3/4 6 8

38. Tony the Triangle Says… You’re so close! Back to Tangent

39. Tony the Triangle Says… That was Fantastic! Back to the Menu On to Applications

40. You’re probably wondering… Find Out!

41. Applications In this picture we can find the height of the tree using our distance from the tree and the angle of inclination.

42. How tall is the tree? We are 20 feet from the tree and our angle of inclination is 45 degrees with our head at ground level. 804020

43. Tony the Triangle Says… Check those applications again! Back to Applications

44. Tony the Triangle Says… Keep on truckin’! Back to the Menu To the final Quiz!

45. Tony the Triangle Says… You can do it!!!! Get ready for 3 questions in a row

46. Question #1 What is the value of r? = pi/4 r 0 1 Sqrt(2) 1

47. Tony the Triangle Says… Back to square 1! Back to the 1 st question

48. Tony the Triangle Says… You got this! Next Question

49. Question #2 What kind of triangle do these trigonometric functions apply to? Equilateral Right neither

50. Tony the Triangle Says… Almost had it. Keep trying! Back to the 1 st question

51. Tony the Triangle Says… Wow! That’s impressive! Next Question

52. Question #3 Which function(s) can be used to find r? = 30 r SineCosine Tangent 1 Sqrt(3) Sine and Cosine

53. Tony the Triangle Says… So close! Try quiz again

54. Tony the Triangle Says… Congrats!!! Review Tony the Triangle would like to congratulate you on mastering these functions!