Trig mini unit

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Trig mini unit

  1. 1. Trigonometric ratios are used with right triangles to solve for missing angles and/or sides.The 3 main trig ratios are:SineCosineTangent
  2. 2. Sides are labeled in reference to a designated angle, θ (“theta”)Hypotenuse: the longest side. Always opposite the right angle.Adjacent: side that is touching the angle θ.Opposite: side across from the angle θ.
  3. 3. name ratio notation sine opp/hyp sin(θ)cosine adj/hyp cos(θ)tangent opp/adj tan(θ)
  4. 4. Set up the ratio using the correct side lengths.Reduce if possible.OR – divide and round your answer.Depends on the directions given.
  5. 5.  Find the value of each trig ratio. sin A= cos A= tan A= sin B= cos B= tan B=
  6. 6. Find the value of each trig ratio to the nearest ten-thousandth.sin R=cos R=tan S=
  7. 7. Inverse trig ratios are used to solve for missing angle measures.They include:sin-1cos-1tan-1On your calculator: hit “2nd” and then the trig button you need
  8. 8. When given a decimal value:Find each angle measure to the nearest degree. sinθ = 0.7193 cosθ = 0.3907 tanθ = 0.6009
  9. 9. When given a triangle:Set up the appropriate ratio, then use the inverse.Find the measure of the indicated angle to the nearest degree.
  10. 10. Find the measure of the indicated angle to the nearest degree.
  11. 11. Find the measure of the indicated angle to the nearest degree.1. tanθ = 1.60032.
  12. 12. Set up trig ratio using the info given.Solve for x.Example:
  13. 13. Find the missing side. Round to the nearest tenth.
  14. 14. Find the missing side. Round to the nearest tenth.
  15. 15. There are two types of “special right triangles.”Their side lengths follow special rules.
  16. 16. Wecan use the PythagoreanTheorem to verify the length of thehypotenuse if both legs are 1.
  17. 17. It follows that for any 45-45-90, the same relationships are true.In general:
  18. 18. Findthe missing side lengths. Leave answers in simplest radical form.
  19. 19. 4√2
  20. 20. Find the missing side lengths.
  21. 21. A 30-60-90 is half of an equilateral triangle.That means the hypotenuse is twice the short leg.We can use the Pythagorean Theorem to find the long leg.
  22. 22. It follows that for any 30-60-90, the same relationships are true.In general: 60º
  23. 23.  Find the missing side lengths. Leave answers in simplest radical form.
  24. 24. x 3√2
  25. 25. Findthe missing side lengths. Leave answers in simplest radical form.
  26. 26. Use trig to find the length of the common side.Then, use trig again to solve for the designated side.Example x 57º 49º 12
  27. 27. 52º12 x 66º
  28. 28. 34º 59º5 x
  29. 29. Remember: A = ½bh for trianglesUse trig to find the length of the base and height.Then find the area.Example:
  30. 30.  Hints for successful problem solving: Draw a picture! Label all given information. Mark the angles or sides you need to find. Use a different variable for each quantity. Create a game plan! Solve using trig. Check that your answer is reasonable. The hypotenuse is always the longest side!
  31. 31. Angle of elevation – measured upward from the horizontal.Angle of depression – measured downward from the horizontal.
  32. 32. A light house is 60 meters high with its base at sea level. From the top of the lighthouse, the angle of depression of a boat is 15 degrees. A. How far is the boat from the foot of the light house? B. How far is the boat from the top of the lighthouse?
  33. 33.  Katieand Sara are attending a theater performance. From her seat, Katie looks down at an angle of 18 degrees to see the orchestra pit. Saras seat is in the balcony directly above Katie. Sara looks down at an angle of 42 degrees to see the pit. The horizontal distance from Katies seat to the pit is 46 ft. What is the vertical distance between Katies seat and Saras seat?

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