1. HW 9
P (19-21, even,
56, 57, 66, even)
P (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

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

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

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

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. 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

11. 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 √ -1
Cot = X √ 3 Y y x 5 -5

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

13. 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 2 y x 5 -5

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

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

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

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

18. 22. Evaluate sec2300–2cos2150+tan45 (Like #22-23)
22 – 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)
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 y x 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)
Csc = R 5
Y -4
Sec = R 5 X
Cot = X
Sin = Y
R 5
Cos = X
Tan = Y X y x 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)
X2 + Y2 = R2
92 + (-2)2 = R2
= R
85 = R2
85 = R
Sin = Y = -285 R
Cos = X = 985 R
Tan = Y = -2
X 9
Csc = R =85 Y
Sec = R = 85 X
Cot = X = Y y x 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)
Csc = R = 2 Y
Sec = R = -2
X 2
Cot = X = 2
X2 + Y2 = R2
(-22)2 + (22)2 = R2
8 + 8 = R2
16 = R2
4 = R
Sin = Y = 2 R
Cos = X = -2
Tan = Y = -1 X y x 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

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

26. 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

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 X
Csc = R 5
Y -2
Sec = R 5
X -1
Cot = X 1
Y 2 y x 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

29. 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

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 X 21
Tan = Y 2√21 Cot = X √21
X Y y x 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