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

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Presentation on theme: "(1,0) (0,1) (-1,0) (0, -1) α (x,y) x y 1 sin(α) = y cos(α) = x (cos(α), sin(α)) (0,0) tan(α) = y/x 2.1 Unit Circle."— Presentation transcript:

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

3 60° 70° 80° 100° 110° 120° 130° 150° 160° 170° 190° 200° 210° 220° 230° 240° 250° 280° 290° 300° 310°.2.4.6.81-.8-.6-.4-.2.2.4.6.8 1 -.2 -.4 -.6 -.8 10° 20° 30° 40° 50° 140° 260° 320° 330° 340° 350°

4 10° 20° 30° 40° 350° 340° 330° 320° 50° 60° 70° 80°100° 110° 120° 130° 140° 150° 160° 170° 190° 200° 210° 220° 230° 240° 250° 260°280° 290° 300° 310°.2.4.6.81-.8-.6-.4-.2.2.4.6.8 1 -.2 -.4 -.6 -.8 Quadrant IQuadrant II Quadrant IIIQuadrant IV Sine + Cosine + Tangent + Sine + Cosine - Tangent - Sine - Cosine - Tangent + Sine - Cosine + Tangent -

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6 2.2 Arc Length and Sectors d (1/7)d C = πd

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

8 α 2.2 Arc Length and Sectors s α s 360 πd =

9 50° 2.2 Arc Length and Sectors s α s 360 πd = 20 in.

10 50° 2.2 Arc Length and Sectors s 50 s 360 40π = 20 in. 200π 360 = = 1.74 in.

11 α 2.2 Arc Length and Sectors k α k 360 πr = 2

12 45° 2.2 Arc Length and Sectors k α k 360 πr = 2 6 ft. 45 k 360 36π = K = 14.14 in. 2

13 2.3 Radian Measure 0 rad. π rad. 2π rad. 1 rad. 2 rad. 3 rad. 4 rad. 5 rad. 6 rad. π 2 rad. 3π3π 2

14 60° 70° 80° 100° 110° 120° 130° 150° 160° 170° 190° 200° 210° 220° 230° 240° 250° 280° 290° 300° 310° 10° 20° 30° 40° 50° 140° 260° 320° 330° 340° 350° π 180° 0, 2π π 2 3π3π 2 π 6 5π5π 6

15 2.4 Inverse Trig Functions and Negative Angles sin (.6) = _____________ ─ 1 36.87˚

16 60° 70° 80° 100° 110° 120° 130° 150° 160° 170° 190° 200° 210° 220° 230° 240° 250° 280° 290° 300° 310°.2.4.6.81-.8-.6-.4-.2.2.4.6.8 1 -.2 -.4 -.6 -.8 10° 20° 30° 40° 50° 140° 260° 320° 330° 340° 350°

17 2.4 Inverse Trig Functions and Negative Angles sin (.6) = ____________________ ─ 1 36.87˚ or 143.13˚ 36.87˚ + 360n 143.13˚ + 360n

18 2.4 Inverse Trig Functions and Negative Angles cos (.4) = ____________________ ─ 1 66.42˚

19 60° 70° 80° 100° 110° 120° 130° 150° 160° 170° 190° 200° 210° 220° 230° 240° 250° 280° 290° 300° 310°.2.4.6.81-.8-.6-.4-.2.2.4.6.8 1 -.2 -.4 -.6 -.8 10° 20° 30° 40° 50° 140° 260° 320° 330° 340° 350°

20 2.4 Inverse Trig Functions and Negative Angles cos (.4) = ____________________ ─ 1 66.42˚ or 293.58˚ 66.42˚ + 360n 293.58˚ + 360n

21 2.4 Inverse Trig Functions and Negative Angles tan (2.5) = _____________ ─ 1 68.2˚

22 60° 70° 80° 100° 110° 120° 130° 150° 160° 170° 190° 200° 210° 220° 230° 240° 250° 280° 290° 300° 310°.2.4.6.81-.8-.6-.4-.2.2.4.6.8 1 -.2 -.4 -.6 -.8 10° 20° 30° 40° 50° 140° 260° 320° 330° 340° 350°

23 2.4 Inverse Trig Functions and Negative Angles tan (2.5) = ____________________ ─ 1 68. 2˚ or 248.2˚ 68.2˚ + 180n

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