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Chapter 2

Chapter 2. Trigonometric Functions. (0,1). •. 2.1 Unit Circle. •. ( x,y ). ( cos ( α ) , sin( α )). 1. y. α. •. •. •. (-1,0). (1,0). (0,0). x. sin( α ) = y. cos ( α ) = x. tan( α ) = y/x. •. (0, -1). 100°. 80°. 1. 110°. 70°. 120°. 60°. 130°. .8. 50°. 140°. 40°.

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Chapter 2

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  1. Chapter 2 Trigonometric Functions

  2. (0,1) • 2.1 Unit Circle • (x,y) (cos(α) , sin(α)) 1 y α • • • (-1,0) (1,0) (0,0) x sin(α) = y cos(α) = x tan(α) = y/x • (0, -1)

  3. 100° 80° 1 110° 70° 120° 60° 130° .8 50° 140° 40° .6 150° 30° .4 20° 160° .2 10° 170° -1 -.8 -.6 -.4 -.2 .2 .4 .6 .8 1 190° 350° -.2 200° 340° -.4 210° 330° -.6 220° 320° 230° 310° -.8 240° 300° 290° 250° -1 260° 280°

  4. 100° 80° • • 1 110° 70° • • 60° 120° • • 50° 130° .8 • • 140° • • 40° Quadrant II .6 Quadrant I • 30° 150° • Sine + Sine + .4 160° • • 20° Cosine - Cosine + Tangent - Tangent + 170° .2 • • 10° -1 -.8 -.6 -.4 -.2 .2 .4 .6 .8 1 • • 350° 190° Quadrant III Quadrant IV -.2 200° • • 340° Sine - Sine - -.4 Cosine - Cosine + • 330° 210° • Tangent + Tangent - -.6 • 320° 220° • • 310° • 230° -.8 • • 240° 300° • • 250° 290° • • 260° 280° -1

  5. 2.2 Arc Length and Sectors C = πd d (1/7)d

  6. 2.2 Arc Length and Sectors r r 2 2 • r 2 (1/7) r r 2 A = πr 2

  7. 2.2 Arc Length and Sectors α s = 360 πd s α •

  8. 2.2 Arc Length and Sectors α s = 360 πd s 50° • 20 in.

  9. 2.2 Arc Length and Sectors 50 s = 360 40π 200π s = 360 = 50° 1.74 in. • 20 in.

  10. 2.2 Arc Length and Sectors α k = 360 πr 2 k α •

  11. 2.2 Arc Length and Sectors α k = 360 πr 2 45 k = 360 36π k 2 K = 14.14 in. 45° • 6 ft.

  12. 2.3 Radian Measure π rad. 2 2 rad. 1 rad. 3 rad. 0 rad. π rad. 2π rad. 6 rad. 4 rad. 5 rad. 3π rad. 2

  13. π 2 100° 80° 110° 70° 120° 60° 130° 50° 140° 40° 5π π 6 150° 30° 6 20° 160° 10° 170° π 180° 0, 2π 190° 350° 200° 340° 210° 330° 220° 320° 230° 310° 240° 300° 290° 250° 260° 3π 280° 2

  14. 2.4 Inverse Trig Functions and Negative Angles 36.87˚ sin (.6) = _____________ ─ 1

  15. 100° 80° 1 110° 70° 120° 60° 130° .8 50° 140° 40° .6 150° 30° .4 20° 160° .2 10° 170° -1 -.8 -.6 -.4 -.2 .2 .4 .6 .8 1 190° 350° -.2 200° 340° -.4 210° 330° -.6 220° 320° 230° 310° -.8 240° 300° 290° 250° -1 260° 280°

  16. 2.4 Inverse Trig Functions and Negative Angles or 143.13˚ 36.87˚ sin (.6) = ____________________ ─ 1 36.87˚ + 360n 143.13˚ + 360n

  17. 2.4 Inverse Trig Functions and Negative Angles 66.42˚ cos (.4) = ____________________ ─ 1

  18. 100° 80° 1 110° 70° 120° 60° 130° .8 50° 140° 40° .6 150° 30° .4 20° 160° .2 10° 170° -1 -.8 -.6 -.4 -.2 .2 .4 .6 .8 1 190° 350° -.2 200° 340° -.4 210° 330° -.6 220° 320° 230° 310° -.8 240° 300° 290° 250° -1 260° 280°

  19. 2.4 Inverse Trig Functions and Negative Angles or 293.58˚ 66.42˚ cos (.4) = ____________________ ─ 1 66.42˚ + 360n 293.58˚ + 360n

  20. 2.4 Inverse Trig Functions and Negative Angles 68.2˚ tan (2.5) = _____________ ─ 1

  21. 100° 80° 1 110° 70° 120° 60° 130° .8 50° 140° 40° .6 150° 30° .4 20° 160° .2 10° 170° -1 -.8 -.6 -.4 -.2 .2 .4 .6 .8 1 190° 350° -.2 200° 340° -.4 210° 330° -.6 220° 320° 230° 310° -.8 240° 300° 290° 250° -1 260° 280°

  22. 2.4 Inverse Trig Functions and Negative Angles or 248.2˚ 68. 2˚ tan (2.5) = ____________________ ─ 1 68.2˚ + 180n

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