11.6: Sine, Cosine, Tangent

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Chapter 11, Section 6: Sine, Cosine, and Tangent. Basic Trig ratios.

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11.6: Sine, Cosine, Tangent

  1. 1. Review/Practice Trig Ratios Chapter 11 Section 6
  2. 2. What is the mnemonic devise that helps us remember the three basic trig ratios? SOH CAH TOA
  3. 3. What is the definition of the sine ratio? opposite leg sin A = hypotenuse
  4. 4. What is the definition of the cosine ratio? adjacent leg cos A = hypotenuse
  5. 5. What is the definition of the tangent ratio? opposite leg tan A = adjacent leg
  6. 6. What trigonometric ratio is needed to solve for x? x 15° 19 opposite leg tan A = adjacent leg
  7. 7. What trigonometric ratio is needed to solve for x? x 38° opposite leg 4.6 sin A = hypotenuse
  8. 8. What trigonometric ratio is needed to solve for x? x 52° 4.6 adjacent leg cos A = hypotenuse
  9. 9. Finding the Decimal or the Degree If you have a decimal and need the degree use INVERSE. Sin(-1), Cos(-1), Tan(-1) If you have a degree and need the decimal use the STANDARD. Sin, Cos, Tan
  10. 10. Find the angle whose tangent is approximately .3057 and round to the nearest degree. 17°
  11. 11. Find the angle whose sine is approximately .7986 and round to the nearest degree. 53°
  12. 12. Find the angle whose cosine is approximately .1564 and round to the nearest degree. 81°
  13. 13. Find the sine of 38 round o to four decimal places. .6157
  14. 14. Find the tangent of 80 o round to four decimal places. 5.6713
  15. 15. Find the cosine of 10 o round to four decimal places. .9848
  16. 16. Identify the trig function needed to solve: x cosine 41° 18
  17. 17. Show the evaluation needed to solve: x cos 41 18 41° = 1 x 18
  18. 18. Solve for x: cos 41 18 = 1 x x cos 41( x) = 18 41° 18 18 x= cos 41 x ≈ 23.85
  19. 19. Identify the trig function needed to solve: 68° x tangent 24
  20. 20. Show the evaluation needed to solve: 68° x tan 68 24 = 1 x 24
  21. 21. Solve for x: tan 68 24 = 1 x x 68° tan 68( x) = 24 24 24 x= tan 68 x ≈ 9.7
  22. 22. Identify the trig function needed to solve: 18.7 x sine 80°
  23. 23. Show the evaluation needed to solve: 18.7 x sin 80 x = 1 18.7 80°
  24. 24. Solve for x: sin 80 x = 1 18.7 18.7 x sin 80(18.7) = x 80° 18.42 ≈ x
  25. 25. Identify the trig function needed to solve: 8.1 cosine x° 3.5
  26. 26. Show the evaluation needed to solve: 8.1 3.5 cos x = 8.1 x° 3.5
  27. 27. Solve for x: 3.5 cos x = 8.1 8.1 −1 cos (3.5 / 8.1) = x x° 64.4° ≈ x 3.5
  28. 28. Identify the trig function needed to solve: x° 5.3 tangent 5.9
  29. 29. Show the evaluation needed to solve: x° 5.3 5.9 tan x = 5.3 5.9
  30. 30. Solve for x: 5.9 tan x = x° 5.3 5.3 −1 tan (5.9 / 5.3) = x 48° ≈ x 5.9
  31. 31. Finished! Finished! Finished! Be sure to know all of this for your test!

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