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HW 9

HW 9. P 56-58 (19-21, 42-50 even, 56, 57, 66, 68-72 even) P100 (12-22 even, 19). 19  Find the angles of smallest possible measure coterminal with the following angles: -51  (Like #2). y. 5. x. -5. -5. 5. y. 5. x. -5. -5. 5.

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HW 9

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  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 5 x -5 -5 5

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

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

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

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

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

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

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

  10. Sin = Y0 R Cos = X 1 R Tan = Y0 X Csc = RØ Y Sec =R1 X Cot = XØ Y (1, 0) y 5 x -5 -5 5 44 Find the values of the six trigonometric functions for an angle of 360. (Like #9-12)(R= 1)

  11. Sin = Y√ 3 R 2 Cos = X-1 R 2 Tan = Y√ 3 X -1 Csc = R2√ 3 Y 3 Sec =R=-2 X √3 2 -1 Cot = X√ 3 Y 3 y 5 x -5 -5 5 12. Find the values of the six trigonometric functions of 120°(Like #13-19)

  12. y 5 x -5 -5 5 12. Find the values of the six trigonometric functions of 120° (Like #13-19) √3 2 -1

  13. Sin = Y= 1 R -2 Cos = X = 1 R -2 Tan = Y1 X Csc = R-2 Y Sec =R-2 X -1 -1 Cot = X 1 2 Y y 5 x -5 -5 5 14. Find the values of the six trigonometric functions of 225°(Like #13-19)

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

  15. 56.Evaluate 4 sec180 – 2sin2270 (Like #20-21) 4 sec180 – 2sin2270 4(-1) – 2(-1)2 - 4 – 2 - 6

  16. 57.Evaluate -cot290°+4sin270°–3tan180°(Like #20-21) -cot290°+4sin270°–3tan180° -(02) + 4(-1) – 3(0) 0 – 4 – 0 -4

  17. 20. Evaluate cos60 + 2sin230 (Like # 22-23) cos60 + 2sin230 ½ + 2(½)2 ½ + 2(1/4) ½ + ½ 1

  18. 22. Evaluate sec2300–2cos2150+tan45 (Like #22-23) sec2300–2cos2150+tan45 22 – 2(-3/2)2 + 1 4 – 2 (3/4) + 1 4 – 1½ + 1 3½

  19. X2 + Y2 = R2 12 + (3)2 = R2 1 + 3 = R2 4 = R2 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 5 x -5 -5 5 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)

  20. Sin = Y-4 R 5 Cos = X3 R 5 Tan = Y-4 X 3 Csc = R 5 Y -4 Sec =R5 X 3 3 Cot = X3 -4 Y -4 y 5 x -5 -5 5 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)

  21. X2 + Y2 = R2 92 + (-2)2 = R2 81 + 4 = R2 9 85 = R2 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 5 x -5 -5 5 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)

  22. X2 + Y2 = R2 (-22)2 + (22)2 = R2 8 + 8 = R2 16 = R2 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 5 x -5 -5 5 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)

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

  24. y 5 x -5 -5 5 66. Find the values of the six trigonometric functions of  (Like #26-29) sin  = √3 , cos  < 0 X2 +√32 = 52 5 X2 + 3 = 25 Sin = Y Csc = RX2 = 22 R Y X = 22 Cos = XSec =R√3 5 R X Tan = Y Cot = X X Y

  25. sin  = √3 , cos  < 0 5 Sin = Y√3 R 5 Cos = X-√22 R 5 Tan = Y-√66 X 22 Csc = R5√3 Y 3 Sec =R- 5√22 X 22 Cot = X-√66 Y 3 5 3 y 5 x -5 -5 5 66. Find the values of the six trigonometric functions of  (Like #26-29)

  26. y 5 x -5 -5 5 68. Find the values of the six trigonometric functions of  (Like #26-29) tan  = 2,  in Q3 X2 + Y2 = R2 (-1)2 + (-2)2 = R2 1 + 4 = R2 5 = R2 5 = R

  27. tan  = 2,  in Q3 Sin = Y-25 R 5 Cos = X-√5 Tan = Y2- X Csc = R5 Y -2 Sec =R5 X -1 Cot = X1 Y 2 y 5 x -5 -5 5 68. Find the values of the six trigonometric functions of  (Like #26-29)

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

  29. y 5 x -5 -5 5 70. Find the values of the six trigonometric functions of  (Like #26-29) sin  = -2,  in Q3 5 X2 + Y2 = R2 X2 + (-2)2 = 52 X2 + 4= 25 X2 = 21 X = 21

  30. y 5 x -5 -5 5 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-√21Sec =R-5√21 R 5X 21 Tan = Y2√21 Cot = X√21 X 21Y 2 -2 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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