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Warm-Up: February 28, 2014

Warm-Up: February 28, 2014. 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?.

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Warm-Up: February 28, 2014

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  1. Warm-Up: February 28, 2014 • 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. Homework Questions?

  3. Trigonometric Functions of Any Angle Section 4.4

  4. 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.

  5. The Six Trigonometric Functions

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

  7. 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.

  8. All Students Take Calculus S A T C

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

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

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

  12. Assignment • Page 474 #1-33 odd

  13. Warm-Up: January 29, 2014 • Given that and find the value of the rest of the trigonometric functions

  14. Homework Questions?

  15. 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

  16. Finding the Reference Angle • Quadrant I: • Quadrant II: • Quadrant III: • Quadrant IV:

  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. 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

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

  21. You-Try #6 • Find the exact value of each of the following:

  22. Trig Values Table

  23. Assignment • Trig Value Table Practice (1 side) • Page 474 #35-65 Odd • No calculators!

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