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8-3 Trigonometry

8-3 Trigonometry. Learning Goal To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles.

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8-3 Trigonometry

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  1. 8-3Trigonometry

  2. Learning GoalTo use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles.

  3. For the remainder of the year your calculator must be in degree mode. All your answers will be wrong if it is not in degree mode.Get out your calculators now. Mr. Bradford will show you.

  4. Trigonometric RatioA ratio of the lengths of sides of a right triangle.

  5. Examples: sine, cosine and tangent.Abbreviations: sin, cos and tan.

  6. Some Old Horse Came A Hopping Through Our Alley

  7. Some Old HorseSin Θ = opposite hypotenuse

  8. Came A HoppingCos Θ = adjacent hypotenuse

  9. Through Our AlleyTan Θ = opposite adjacent

  10. Θ is the measure of an acute angle in a right triangle.

  11. Step 1Label the Hypotenuse.(across from the right angle) 43˚ hyp x 10

  12. Step 2Put an arc over the angle that has a number or variable with a degree symbol. 43˚ hyp x 10

  13. Step 3Label the other side the arc touches: Adjacent. 43˚ hyp x adj 10

  14. Step 4Label the remaining side: Opposite. 43˚ hyp x adj 10 opp

  15. Step 5Decide if sin, cos or tan. 43˚ hyp x adj 10 opp

  16. Step 6Create equation. 10 tan 43 = — x 43˚ hyp x adj 10 opp

  17. Step 7Solve. 10 tan 43 = — x

  18. Step 7Solve. 10 tan 43 = — x 10 .9325 = — x

  19. Step 7Solve. 10 tan 43 = — x ( ) ( ) 10 .9325 = — x x x

  20. Step 7Solve. 10 tan 43 = — x ( ) ( ) 10 .9325 = — x x x .9325x = 10

  21. Step 7Solve. 10 tan 43 = — x ( ) ( ) 10 .9325 = — x x x .9325x = 10 .9325 .9325

  22. Step 7Solve. 10 tan 43 = — x ( ) ( ) 10 .9325 = — x x x .9325x = 10 .9325 .9325 x = 10.7

  23. Lets try another. 16 12 x˚

  24. Lets try another. 12 sin x = — 16

  25. Lets try another. 12 sin x = — 16 sin x = .75

  26. Lets try another. 12 sin x = — 16 sin x = .75 sin-1(sin x) = sin-1.75

  27. Lets try another. 12 sin x = — 16 sin x = .75 sin-1(sin x) = sin-1.75

  28. Lets try another. 12 sin x = — 16 sin x = .75 sin-1(sin x) = sin-1.75 x = 48.6

  29. Trigonometry Worksheet5 Points: 100% Complete 4 Points: 80% Complete 3 Points: 60% Complete 2 Points: 40% Complete 1 Point: 20% Complete

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