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HW 9 P 56-58 (19-21, 42-50 even, 56, 57, 66, 68-72 even) P100 (12-22 even, 19)

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Presentation on theme: "HW 9 P 56-58 (19-21, 42-50 even, 56, 57, 66, 68-72 even) P100 (12-22 even, 19)"— Presentation transcript:

1 HW 9 P 56-58 (19-21, 42-50 even, 56, 57, 66, 68-72 even) P100 (12-22 even, 19)

2 19  Find the angles of smallest possible measure coterminal with the following angles: -51  (Like #2) y x 5 5 -5

3 19  Find the angles of smallest possible measure coterminal with the following angles: -51  (Like #2) 360° -51° 309° y x 5 5 -5

4 20  Find the angles of smallest possible measure coterminal with the following angles: -174  (Like #2) y x 5 5 -5

5 20  Find the angles of smallest possible measure coterminal with the following angles: -174  (Like #2) 360° -174  186° y x 5 5 -5

6 21  Find the angles of smallest possible measure coterminal with the following angles: 792  (Like #1) y x 5 5 -5

7 21  Find the angles of smallest possible measure coterminal with the following angles: 792  (Like #1) 792  – 720  72  y x 5 5 -5

8 72.If for , sin  0, in what quadrant must  lie? What is the sign of tan  ? (Like # 3-8) sin  0 tan  is ___________in Quadrant lV.

9 72.If for , sin  0, in what quadrant must  lie? What is the sign of tan  ? (Like # 3-8) sin  0 lll, lV l, lV lV tan  is negative in Quadrant lV.

10 44  Find the values of the six trigonometric functions for an angle of 360 . (Like #9-12)(R = 1) Sin = Y 0 R Cos = X 1 R Tan = Y 0 X Csc = R Ø Y Sec = R 1 X Cot = X Ø Y (1, 0) y x 5 5 -5

11 12. Find the values of the six trigonometric functions of 120° (Like #13-19) Sin = Y √ 3 R 2 Cos = X -1 R 2 Tan = Y √ 3 X -1 Csc = R 2√ 3 Y 3 Sec = R = -2 X √3 2 Cot = X √ 3 Y 3 y x 5 5 -5

12 12. Find the values of the six trigonometric functions of 120° (Like #13-19) √3 2 y x 5 5 -5 Sin √ 3 2Csc 2√ 3 3 Cos 2Sec - 2 Tan -√ 3 Cot -√ 3 3

13 14. Find the values of the six trigonometric functions of 225° (Like #13-19) Sin = Y = 1 R -  2 Cos = X = 1 R -  2 Tan = Y 1 X Csc = R -  2 Y Sec = R -  2 X Cot = X 1 2 Y y x 5 5 -5

14 14. Find the values of the six trigonometric functions of 225° (Like #13-19) -1  2 y x 5 5 -5 Sin -  2 2Csc -2-2 Cos -  2 2Sec -2-2 Tan 1Cot 1

15 56.Evaluate 4 sec180 – 2sin 2 270 (Like #20-21) 4 sec180 – 2sin 2 270 4(-1) – 2(-1) 2 - 4 – 2 - 6

16 57.Evaluate -cot 2 90°+4sin270°–3tan180° (Like #20-21) -cot 2 90°+4sin270°–3tan180° -(0 2 ) + 4(-1) – 3(0) 0 – 4 – 0 -4

17 20. Evaluate cos60 + 2sin 2 30 (Like # 22-23) cos60 + 2sin 2 30 ½ + 2(½) 2 ½ + 2(1/4) ½ + ½ 1

18 22. Evaluate sec 2 300–2cos 2 150+tan45 (Like #22-23) sec 2 300–2cos 2 150+tan45 2 2 – 2(-  3/2) 2 + 1 4 – 2 (3/4) + 1 4 – 1½ + 1 3½

19 42  The terminal side of an angle  in standard position goes through the point (1,-  3 ). Find the values of the six trigonometric functions of  (Like #24-25) X 2 + Y 2 = R 2 1 2 + (  3) 2 = R 2 1 + 3 = R 2 4 = R 2 2 = R Sin = Y =-  3 R 2 Cos = X = 1 R 2 Tan = Y =-  3 X Csc = R =-2  3 Y 3 Sec = R = 2 X 1 1 -  3 Cot = X =-  3 Y 3 y x 5 5 -5

20 46  The terminal side of an angle  in standard position goes through the point (3,-4). Find the values of the six trigonometric functions of  (Like #24-25) Sin = Y -4 R 5 Cos = X 3 R 5 Tan = Y -4 X 3 Csc = R 5 Y -4 Sec = R 5 X 3 3 Cot = X 3 -4 Y -4 y x 5 5 -5

21 48  The terminal side of an angle  in standard position goes through the point (9,-2). Find the values of the six trigonometric functions of  (Like #24-25) X 2 + Y 2 = R 2 9 2 + (-2) 2 = R 2 81 + 4 = R 2 9 85 = R 2  85 = R Sin = Y = -2  85 R 85 Cos = X = 9  85 R 85 Tan = Y = -2 X 9 Csc = R =  85 Y -2 Sec = R =  85 X 9 Cot = X = 9 9 Y -2 -2 y x 5 5 -5

22 50  The terminal side of an angle  in standard position goes through the point (-2  2,2  2 ). Find the values of the six trigonometric functions of  (Like #24-25) X 2 + Y 2 = R 2 (-2  2) 2 + (2  2) 2 = R 2 8 + 8 = R 2 16 = R 2 4 = R Sin = Y =  2 R 2 Cos = X = -  2 R 2 Tan = Y = -1 X Csc = R =  2 Y Sec = R =  -2 X 2  2 Cot = X = -1 -2  2 Y y x 5 5 -5

23 66. Find the values of the six trigonometric functions of  (Like #26-29) sin  = √3, cos  < 0 5 y x 5 5 -5

24 66. Find the values of the six trigonometric functions of  (Like #26-29) sin  = √3, cos  < 0 X 2 +√3 2 = 5 2 5 X 2 + 3 = 25 Sin = Y Csc = R X 2 = 22 R Y X =  22 Cos = X Sec = R √3 5 R X Tan = Y Cot = X X Y y x 5 5 -5

25 66. Find the values of the six trigonometric functions of  (Like #26-29) sin  = √3, cos  < 0 5 Sin = Y √3 R 5 Cos = X -√22 R 5 Tan = Y -√66 X 22 Csc = R 5√3 Y 3 Sec = R - 5√22 X 22 Cot = X -√66 Y 3 5  3 y x 5 5 -5

26 68. Find the values of the six trigonometric functions of  (Like #26-29) tan  = 2,  in Q3 X 2 + Y 2 = R 2 (-1) 2 + (-2) 2 = R 2 1 + 4 = R 2 5 = R 2  5 = R y x 5 5 -5

27 68. Find the values of the six trigonometric functions of  (Like #26-29) tan  = 2,  in Q3 Sin = Y -2  5 R 5 Cos = X -√5 Tan = Y 2 - X Csc = R  5 Y -2 Sec = R  5 X -1 Cot = X 1 Y 2 y x 5 5 -5

28 70. Find the values of the six trigonometric functions of  (Like #26-29) sin  = -2,  in Q3 5 y x 5 5 -5

29 70. Find the values of the six trigonometric functions of  (Like #26-29) sin  = -2,  in Q3 5 X 2 + Y 2 = R 2 X 2 + (-2) 2 = 5 2 X 2 + 4 = 25 X 2 = 21 X =  21 y x 5 5 -5

30 70. Find the values of the six trigonometric functions of  (Like #26-29) sin  = -2,  in Q3 5 Sin = Y Csc = R -5 R Y 2 Cos = X -√21 Sec = R -5√21 R 5 X 21 Tan = Y 2√21 Cot = X √21 X 21 Y 2 -2 5 y x 5 5 -5

31 Find all values of  in [0 , 360  ) and has the given function value. 16. sin  = -1/2 210 , 330  18. cot  = -1 135 , 315  19. sec  = -2  3/3 150 , 210 


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