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TRIGONOMETRY

TRIGONOMETRY. Let’s have some fun!. With Tony the Triangle!!!. Click me!. Let’s Get Started!. Where to start…. Cosine. Sine. Tangent. Click here to begin. SOH-CAH-TOA. In Trigonometry the three basic functions that we will be learning about can be remembered by the pneumonic below:

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TRIGONOMETRY

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

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

  3. 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!

  4. 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!

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

  6. The Sine Function Sine comes from the SOH part of soh-cah-toa Sine equals Opposite over Hypotenuse

  7. SOH Opposite Hypotenuse Opposite Sin( )= Hypotenuse

  8. 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.

  9. =30 degrees Opp. Side = 1 Opposite Sin(30)= 1/hypotenuse (Hypotenuse)(Sin(30))=1 Hypotenuse = 2

  10. 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.

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

  12. 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.

  13. =60 degrees Hypotenuse= 2 Hypotenuse Sin(60)= opposite side/2 2(Sin(30))=Opposite side Opposite side = 1

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

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

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

  17. The Cosine Function Cosine comes from the CAH part of soh-cah-toa Cosine equals Adjacent over Hypotenuse

  18. CAH Hypotenuse Adjacent Adjacent Cos( )= Hypotenuse

  19. 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.

  20. =30 degrees Adj. Side = sqrt(3) Adjacent Cos(30)= sqrt(3)/Hypotenuse (Hypotenuse)(Cos(30))=sqrt(3) Hypotenuse = 2

  21. 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.

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

  23. 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.

  24. =60 degrees Hypotenuse= 2 Hypotenuse Sin(60)= Adjacent side/2 2(Sin(30))=Adjacent Side Adjacent side = 1

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

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

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

  28. The Tangent Function Tangent comes from the TOA part of soh-cah-toa Tangent equals Opposite over Adjacent

  29. TOA Opposite Adjacent Opposite Tan( )= Adjacent

  30. 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.

  31. =30 degrees Adj. Side = sqrt(3) Adjacent Tan(30)= (1/sqrt(3))/Opposite (Opposite)(Tan(30))=(1/sqrt(3)) Opposite=1

  32. 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.

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

  34. 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.

  35. =45 degrees Opposite= 2 Tan(45)= 2/(Adjacent Side) 2=(Tan(45))(Adjacent Side) Adjacent side = 2

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

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

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

  39. You’re probably wondering… How does this affect me? Why should I care? When will we ever us this? Find Out!

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

  41. 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. 20 40 80

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

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

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

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

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

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

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

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

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

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