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 x 5 -5

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

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

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

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

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.

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.

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 Tan = Y 0 X Csc = R Ø Y Sec = R 1 X Cot = X Ø Y (1, 0) y x 5 -5

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

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

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

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

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

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

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

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

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) 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 x 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) Csc = R 5 Y -4 Sec = R 5 X 3 3 Cot = X 3 -4 Sin = Y -4 R 5 Cos = X 3 Tan = Y -4 X 3 y x 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) 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 x 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) Csc = R = 2 Y Sec = R = -2 X 22 Cot = X = -1 -22 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 Tan = Y = -1 X y x 5 -5

66. Find the values of the six trigonometric functions of  (Like #26-29) sin  = √3 , cos  < 0 5 y x 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 = R X2 = 22 R Y X = 22 Cos = X Sec = R √3 5 R X Tan = Y Cot = X X Y y x 5 -5

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

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 y x 5 -5

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

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

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