CHAPTER 6, FORM A
TRIGONOMETRY
NAME __________________________
DATE __________________________
Do not use a calculator for this test except where indicated.
1. State the domain and range of sin
1
1. D: __________________________
R: __________________________
x.
For Problems 2-3, give the exact real number value of y. For Problem 4,
use a calculator to give an approximate value to the nearest hundredth.
1
2
2. ____________________________
3
3
3. ____________________________
4. y = arcsec (–1.5)
4. ____________________________
2. y
csc
3. y
arccot
Find each of the following.
3
4
5. tan arccos
6. sin
1
tan
π
1
csc
6. ____________________________
4
7. sin arccos
8. csc
5. ____________________________
1
3
arcsin
5π
4
2
5
7. ____________________________
5π
. Explain.
4
8. ____________________________
Solve the equation for solutions in the interval [0°, 360°).
Use a calculator for Problem 12; give the answer to the
nearest hundredth of a degree.
9. cos 3 θ
10. tan θ
11. 2 cos θ
cos θ
9. ____________________________
2sin θ
10. ____________________________
2
11. ____________________________
0
12. 6 sin θ + 2 = 0
12. ____________________________
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CHAPTER 6, FORM A, PAGE 2
Solve the equation for solutions in the interval [0, 2 ).
Use a calculator for Problem 16; give the answer to three
decimal places.
13. 2 cos 2 x 1
13. ____________________________
3cos x
14. cos 2x = sin x
15. sin
1
x
2
16. sin 2 x
14. ____________________________
cos x
15. ____________________________
1
4
16. ____________________________
Solve the equation for x.
17. y = 2 sin 3x
17. ____________________________
18. 5y = 4 tan x + 1
18. ____________________________
Solve the equation.
19. tan 1 3x
π
19. ____________________________
4
20. arccos x – arccot
6
5
20. ____________________________
0
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107
CHAPTER 6, FORM B
TRIGONOMETRY
NAME __________________________
DATE __________________________
Do not use a calculator for this test except where indicated.
1. State the domain and range of cos
1
1. D: __________________________
R: __________________________
x.
For Problems 2-3, give the exact real number value of y. For Problem 4,
use a calculator to give an approximate value to the nearest hundredth.
2. y
cos 1 0
3. y
sin
4. y
sec 1 ( 3)
1
2. ____________________________
1
2
3. ____________________________
4. ____________________________
Find each of the following.
5. csc arcsin
6. cos
1
tan
9
15
π
1
6. ____________________________
4
2
3
7. sin arccos
8. sec
5. ____________________________
sec
arcsin
π
π
3
3
1
4
7. ____________________________
8. ____________________________
. Explain.
Solve the equation for solutions in the interval [0°, 360°).
Use a calculator for Problem 12; give the answer to the
nearest hundredth of a degree.
9.
3 tan θ
2sin θ
10. 2 cos θ
3
11. sec 2 θ
2 sec θ
12. sin 2 θ
1
3
9. ____________________________
10. ____________________________
0
11. ____________________________
0
12. ____________________________
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108
CHAPTER 6, FORM B, PAGE 2
Solve the equation for solutions in the interval [0, 2 ).
Use a calculator for Problem 16; give the answer to three
decimal places.
13. 2 sin 2 x sin x
14. 3 tan 2 x
15. sin
x
2
13. ____________________________
1
14. ____________________________
0
1 sin
16. cos 2 x
x
2
15. ____________________________
3
4
16. ____________________________
Solve the equation for x.
17. y = 3 cos 2x
17. ____________________________
18. 3y = 5 sin (x – 4)
18. ____________________________
Solve the equation.
19. sin 1 2 x
20. arctan x
π
19. ____________________________
4
arccos
5
13
20. ____________________________
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109
CHAPTER 6, FORM C
TRIGONOMETRY
NAME __________________________
DATE __________________________
Do not use a calculator for this test except where indicated.
1. State the domain and range of tan
1
1. D: __________________________
R: __________________________
x.
For Problems 2-3, give the exact real number value of y. For Problem 4,
use a calculator to give an approximate value to the nearest hundredth.
2. y
tan 1 ( 1)
2. ____________________________
3. y
sec 1 ( 2)
3. ____________________________
4. y = arccos (–0.8)
4. ____________________________
Find each of the following.
5. tan arcsin
6. cos
1
sin
1
3
5. ____________________________
π
6. ____________________________
3
3
4
arccos
π
π
6
6
7. cos arcsin
8. cos
1
cos
2
3
7. ____________________________
8. ____________________________
. Explain.
Solve the equation for solutions in the interval [0°, 360°).
Use a calculator for Problem 12; give the answer to the
nearest hundredth of a degree.
9. 2 sec θ – 4 = 0
10. 2 cos θ
9. ____________________________
cot θ
11. cot 2 θ
cot θ
12. 3sin 2 θ
2
10. ____________________________
11. ____________________________
0
12. ____________________________
0
Solve the equation for solutions in the interval [0, 2 ).
Use a calculator for Problem 16; give the answer to three
decimal places.
13. 2 sin 2 x
3sin x 1
13. ____________________________
0
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CHAPTER 6, FORM C, PAGE 2
x
14. tan
sin x
2
14. ____________________________
15. sin 2x = sin x
15. ____________________________
16. 5 sin 2x = 3
16. ____________________________
Solve the equation for x.
17. y
2 tan
x
3
17. ____________________________
18. 7y = 3 cos (x + 4)
18. ____________________________
Solve the equation.
19. tan 1 3x
20. arcsin x
π
4
19. ____________________________
0
arccos
7
25
20. ____________________________
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111