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Trigonometry

Trigonometry. Sine. S – O – H. Cosine. C – A – H. Tangent. T – O – A. a ⁰ + b ⁰ = 90 ⁰. a ⁰ + b ⁰ = 90 ⁰. a ⁰ + b ⁰ = 90 ⁰. Inverse Sine. Arcsin (x) or Sin -1 (x). Sin -1 (a/c)= α ⁰. Inverse Cosine. Arccos (x) or Cos -1 (x). Cos -1 (b/c)= α ⁰. Inverse Tangent.

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Trigonometry

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  1. Trigonometry

  2. Sine S – O – H

  3. Cosine C – A – H

  4. Tangent T – O – A

  5. a⁰ + b⁰ = 90⁰

  6. a⁰ + b⁰ = 90⁰

  7. a⁰ + b⁰ = 90⁰

  8. Inverse Sine Arcsin (x) or Sin-1(x) Sin-1(a/c)=α⁰

  9. Inverse Cosine Arccos (x) or Cos-1(x) Cos-1(b/c)=α⁰

  10. Inverse Tangent Arctan (x) or Tan-1(x) Tan-1(a/b)=α⁰

  11. Solving Right Triangles Given two sides. 1) Use the Pythagorean Theorem to find 3rd side. 2) Use preferred inverse trig ratio to find angles.

  12. Solving Right Triangles Given one side and one angle. 1) Use preferred trig ratio to find 2nd side. 2) Use the Pythagorean Theorem to find 3rd side. 3) Use Triangle Sum Theorem to find 2nd angle.

  13. Similar Right Triangles Separate the triangles! Small Triangle Large Triangle Medium Triangle

  14. What are the angles? Remember,a + b = 90°

  15. Example: Given Sides Small Triangle Large Triangle Medium Triangle Now complete the large triangle. The small triangle is now complete. The small triangle is similar to the medium triangle. Which triangle has 2 quantities? 152 + b2 = 252 b =16 92+122=a2 What do you know about the other triangles?

  16. Example: Given Angle & Side. Remember, when you know one angle, you can find the others. Complete the medium triangle. Finally, complete the large side. Which triangle has the side? 10√3 10 20

  17. The Shadow Problem The Washington Monument casts a shadow… A tree casts a shadow… A flagpole casts a shadow… The Washington Monument is 169m tall. If the shadow is 100m long, what angle does the sun’s rays make with the monument? Round to the nearest 100th. If the flagpole is 35’ tall and the sun’s rays makes an angle of of 40⁰ with the flagpole, how long is the shadow? Round to the nearest 10th. If the shadow is 285’ long and the sun’s rays makes an angle of 55⁰ with the tree, how tall is the tree? Round to the nearest foot.

  18. Angles of Elevation/Depression Which one you use depends on your point of view. However, they are essentially the same thing. Why?

  19. Angles of Elevation The Ramp Problem The smaller the angle, the easier it is to push something up the ramp. If the bed of a truck is 3.5’ high and you want a ramp with a 10⁰ angle, how long (along the diagonal) does the ramp have to be? Round to the 10th.

  20. Angles of Depression The Lighthouse Problem A lighthouse keeper is looking at a boat at sea. If his line of sight is 20⁰ from the horizontal and the light is 95’ from sea level, how far is the boat from shore? Round to the nearest foot.

  21. Angles of ???? The Ski Slope Problem A downhill racer skis a mountain with a 28⁰ grade (against the horizontal). If the vertical height of the slope is 4,500‘ and he completed the run in 2.5 minutes, how fast did he go? Find the answer in feet/minute, then mph. Round to the nearest mile.

  22. Angles of ???? The Kite/Balloon/Plane Problem During the Civil War, the Union Army used hot air balloons for reconnaissance. If the balloonist is 1000’ high and he sees cannons when the angle of his line of sight is 12⁰, how far are the cannons from his base? Round to the nearest foot.

  23. Which to use? Sin or Cos or Tan? Do you have or do you want the hypotenuse? Which do you have/want – opp or adj? Yes Opp Use Sine. If you want the angle use inverse sine. No Adj Use tangent. If you want the angle, use inverse tangent. Use Cosine. If you want the angle use inverse cosine.

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