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Unit 10: Lesson #1 Textbook 9-1 and 9-1

Unit 10: Lesson #1 Textbook 9-1 and 9-1. To start out please pick up Lesson #1 Investigation from the front of the classroom. Trigonometric Ratios. A. A. A. 2. 5. 25 . B. C. 4.3. 40 . B. C. 5.95. 60 . C. B. 4. Warm-Up:. Tan 25  = 0.4663. Tan 40  = 0.8391.

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Unit 10: Lesson #1 Textbook 9-1 and 9-1

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  1. Unit 10: Lesson #1Textbook 9-1 and 9-1 To start out please pick up Lesson #1 Investigation from the front of the classroom. Trigonometric Ratios

  2. A A A 2 5 25 B C 4.3 40 B C 5.95 60 C B 4 Warm-Up: Tan 25 = 0.4663 Tan 40 = 0.8391 Tan 60 = 1.7321

  3. Tan 20 = 0.4663 Tan 40 = 0.8391 Tan 60 = 1.7321

  4. What does it all mean? Trigonometry is the study of side length ratios of right triangles. There are 3 ratios that the Greeks studied and gave names to: Tangent Sine Cosine The values of these ratios are recorded in the chart from your book and in your calculator. So, trigonometry is a way to find parts of right triangles when using the Pythagorean Theorem doesn’t work.

  5. Important Vocabulary

  6. Opposite and Adjacent are relative to the angle • The 4cm side is opposite to A • The 6cm side is adjacent to A • The 6cm side is opposite to B • The 4cm side is adjacent to B

  7. SOH CAH TOA • SOH • SineOppositeHypoteneuse • (Sine of angle =Opposite side / Hypotenuse) • CAH • CosineAdajcentHypotenuse • (Cosine of angle = Adjacent side / hypotenuse) • TOA • TangentOppositeAdjacent • (Tangent of angle = Opposite side / adjacent side)

  8. Trig Rap http://www.youtube.com/watch?v=NeIm_aSFd3I

  9. Example #1 (A) tan x = (B) tan y = (C) sin x = (D) cosx = (E) sin y = (F) cosy =

  10. Finding Missing Values in Trig Ratios First, remember that tan 35 has some other value ( 35). The calculator knows the value, so we just type tan 35 when solving. tan 35 = If it helps, treat this problem like a proportion by putting a 1 under the tan 35. Cross multiply! Don’t convert this into a number. Type tan 35 into your calculator just the way it is. Round your final answer to a tenth (one decimal).

  11. Example #2: Finding Missing Values in Trig Ratios tan 18 = Don’t convert this into a number. Type it into your calculator just the way it is. x  28.3

  12. tan 55 = Finding Missing Triangle Parts Using Trig Find the value of x. Set up the tangent ratio

  13. Example #1: Finding Missing Lengths Using Trig sin 32 = a a  8.2 k  6.4

  14. Example #2: Finding Missing Lengths Using Trig k g g  13.8 k  12.9

  15. Example #3: Finding Missing Lengths Using Trig cos 41 = Tan 50 = x  8.3 x  7.7

  16. 25m 70° 2m Emergency!!! A ladder on a fire truck can be turned to a maximum angle of 70° and can be extended to a maximum length of 25m. If the base of the ladder is mounted on the fire truck 2m above the ground, how high above the ground will the ladder reach?

  17. x 6° 800m Fasten your seatbelts A small plane takes off from an airport and rises uniformly at an angle of 6° with the horizontal ground. After it has traveled over a horizontal distance of 800m, what is the altitude of the plane to the nearest meter?

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