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D. Trigonometry

D. Trigonometry. Math 10: Foundations and Pre-Calculus FP10.4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles. Key Terms:. Find the definition of each of the following terms : Angle of Inclination Tangent Ratio

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D. Trigonometry

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  1. D. Trigonometry Math 10: Foundations and Pre-Calculus FP10.4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

  2. Key Terms: • Find the definition of each of the following terms: • Angle of Inclination • Tangent Ratio • Sine Ratio • Cosine Ratio • Indirect Measurement • Angle of Elevation • Angle of Depression

  3. 1. The Tangent Ratio • FP10.4 • Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

  4. 1. The Tangent Ratio • Remember the Tan ratio? • What is the tan ratio and what do we use it for?

  5. The value of the tangent ratio is usually expressed as a decimal that compares the lengths of the sides

  6. Example

  7. You can use a scientific calculator to determine the measure of an acute angle when you know the value tan ratio • The tan-1 or Invtan on your calculator does this for you

  8. Example

  9. Example

  10. Example

  11. Practice • Ex. 2.1 (p. 74) #1-20 #6-23

  12. 2. Calculating Length with Tangent Ratio • FP10.4 • Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

  13. The tangent ratio is a powerful tool we can use to calculate the length of a leg of a right triangle • We are measuring indirectly when we measure this way

  14. We can find the length of a leg of a triangle by setting up the tangent formula, as long as we have one of the acute angles and the legs

  15. Example

  16. Example

  17. Example 3

  18. Practice • Ex. 2.2 (p. 81) #1-14 #1-4, 6-16

  19. 3. Sine and Cosine Ratios • FP10.4 • Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

  20. In a right triangle, the ratios that relate each leg to the hypotenuse depend only on the measure of the acute angle not the size of the triangle • These ratios are called the sine and cosine ratios

  21. The sine ratio is written sin θ • The cosine ratio is written cos θ

  22. The sine, cosine and tangent ratios are called the primary trig ratio • The values of the trig ratios are often expressed as decimals

  23. Example

  24. Example

  25. Example

  26. Practice • Ex. 2.4 (p. 94) #1-15 #1-3, 5-17

  27. 4. Using Sine and Cosine to find Length • FP10.4 • Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

  28. 4. Using Sine and Cosine to find Length

  29. Construct Understanding p. 97

  30. We can use the sin and cos ratios to write an equation that we can solve to calculate the length of a leg in a right triangle • When the measure of one acute angle and the hypotenuse are know

  31. Example

  32. The sin and cosine ratios can be used to calculate the measure of the hypotenuse • When the measure of one acute angle and the length of one of the legs are known

  33. Example

  34. Example

  35. Practice • Ex. 2.5 (p. 101) #1-12 #1-14

  36. 5. Applying Trig • FP10.4 • Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

  37. 5. Applying Trig

  38. Construct Understanding p. 105

  39. When we calculate the measures of all the angles and all the side lengths in a right triangle, we solve the triangles.

  40. We can use any of the three primary trig ratios to do this.

  41. Example

  42. Example

  43. Example

  44. Practice • Ex. 2.6 (p. 110) #1-14 #1-2, 5-16

  45. 6. Problems with More Triangles • FP10.4 • Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

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