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Warm-Up: March 4, 2011

Warm-Up: March 4, 2011. A man is standing at the top of a cliff, 25 meters above the water below. He is looking out at a boat in the distance. The angle of depression is 30˚. How far away from the bottom of the cliff is the boat? How far away is the boat from the man?. Retakes.

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Warm-Up: March 4, 2011

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  1. Warm-Up: March 4, 2011 • A man is standing at the top of a cliff, 25 meters above the water below. He is looking out at a boat in the distance. The angle of depression is 30˚. • How far away from the bottom of the cliff is the boat? • How far away is the boat from the man?

  2. Retakes • Lunch today for unit circle quiz only • Next week: • M, Th, F after school: Ch 3 test or unit circle quiz • Monday lunch, Tuesday after school, Wednesday after school, Thursday lunch, Friday lunch: unit circle quiz only • Following week: • M, W, Th, F lunch: Unit circle quiz only • After school availability TBD

  3. Homework Questions?

  4. Unit Circle Quiz • No calculators • No notes • No talking. If you appear to be talking while any quiz is out, you will receive a zero. • The quiz is worth 20 points. If you get everything right, you get 20/20. If you do not, you get zero points, but you can retake it as many times as you need to get everything right (and the 20 points) • If you get them all correct before the Chapter 4 test, you can use it on that test.

  5. Trigonometric Functions of Any Angle Section 4.4

  6. What’s New? • We are no longer restricting ourselves to points on the unit circle. • Points can now be any distance “r” away from the origin • Points are still always on the terminal side of θ. Initial side is still the positive x-axis.

  7. The Six Trigonometric Functions

  8. Example 1 • Let P=(-5, -12) be a point on the terminal side of θ. Find each of the six trigonometric functions of θ.

  9. You-Try #1 • Let P=(4, -3) be a point on the terminal side of θ. Find each of the six trigonometric functions of θ.

  10. All Students Take Calculus S A T C

  11. You-Try #3 • If tan θ >0 and cosθ < 0, in which quadrant does θ lie?

  12. Example 4 • Given that and find the value of the rest of the trigonometric functions

  13. You-Try #4 • Given that and find the value of the rest of the trigonometric functions

  14. Warm-Up: March 7, 2011 • Given that and find the value of the rest of the trigonometric functions

  15. Homework Questions?

  16. Reference Angles • We like dealing with acute angles (0˚<θ<90˚). • We can often find trig functions of non-acute angles by using an acute reference angle • Let θ be a non-acute angle in standard position that lies in a quadrant (not on an axis) • Its reference angle is the positive acute angle θ’ formed by the terminal side of θ and the x-axis

  17. Example 5 • Find the reference angle θ’ for each of the following angles:

  18. You-Try #5 • Find the reference angle θ’ for each of the following angles:

  19. Warm-Up: March 11, 2011

  20. Using Reference Angles to Evaluate Trigonometric Functions • Find the associated reference angle, θ’ • Find the trig function value of θ’ • Use the quadrant which θ lies in to choose the appropriate sign to the value found in step 2

  21. Example 6 • Find the exact value of each of the following:

  22. Example 6 • Find the exact value of each of the following:

  23. Assignment • Page 474 #1-65 Every Other Odd • No calculators!

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