1. No category

13.3B Worksheet
Name _______________________________
Assignment # _____
1. Evaluate the six trig functions of the angle θ .
Find the missing side lengths x and y
2.
θ
3.
y
Use a calculator to evaluate the trig function. Round the result to 4 decimal places.
4. tan 100
5. sin 510
6. csc 180
7. sec 290
8. cot 380
Solve right triangle ABC
10.
9. cos 100
11.
Draw an angle with the given measure in std position. Find one positive angle and one negative angle
coterminal with the given angle.
4π
π
12. 1050
13. -750
14.
15. −
3
4
Rewrite each degree measure in radians and each radian measure in degrees.
3π
5π
16. 3150
17. −
18.
4
6
Evaluate the six trig functions of the quadrantal angle θ .
20. θ = −2700
21. θ = −900
22. θ = −1800
19. −750
23. θ = 3600
24. Find the arc length of a sector with the given radius 8m and central angle θ = 2100
Evaluate the trig function using a calculator if necessary. If possible, give an exact answer.
π
π
π
2π
25. cot
26. tan
27. csc
28. cos
3
3
8
5
29. sin
7π
15
30. sec
3π
8
31. cot
π
32. csc
6
π
4
Use the given point on the terminal side of an angle θ in standard position. Evaluate the 6 trig functions of θ .
33. (3 , – 2)
34. − 3,1
(
Sketch the angle. Then find its reference angle.
35. −5100
36. 3450
39.
21π
4
40.
20π
3
Evaluate the function without using a calculator.
43. sec 2250
44. cos (– 2250)
47. cos
15π
4
48. csc
5π
6
)
37. 2000
41. −
11π
6
45. csc (– 1200)
49. cot
11π
6
38. – 2400
42.
2π
3
46. tan 2400
⎛ 4π ⎞
50. sec ⎜ −
⎟
⎝ 3 ⎠
Use a calculator to evaluate the function. Round the result to four decimal places.
18π
⎛ 9π ⎞
51. csc 2.30
52. cot 2400
53. sec ⎜ −
54. csc
⎟
5
⎝ 2 ⎠
Answers:
sin θ = 10 /13;csc θ = 13 /10
1. cos θ = 69 /13;sec θ = 13 69 / 69
2. x = 10; y = 5 3
3. x = y = 4 2
tan θ = 10 69 / 69;cot θ = 69 /10
4. 0.1763
5. 0.7771
6. 3.2361
7. 1.1434
8. 1.2799
9. 0.9848
10. ∠C = 33o; a ≈ 10.1; c ≈ 6.5
11. b ≈ 14.3;c ≈ 7.8;∠C = 33
12. 465 o ; -255 o
13. 285 o ; -435 o
14. −2π / 3;10π / 3
15. 7π / 4; −9π / 4
16. 7π / 4
17. -135 o
18. 150 o
19. −5π /12
sin θ = 1;csc θ = 1
sin θ = −1;csc θ = −1
20. cos θ = 0;sec θ = undef
21. cos θ = 0;sec θ = undef
tan θ = undef ;cot θ = 0
tan θ = undef ;cot θ = 0
sin θ = 0;csc θ = undef
sin θ = 0;csc θ = undef
22. cos θ = 0 = −1;sec θ = −1
23. cos θ = 0 = 1;sec θ = 1
tan θ = 0;cot θ = undef
24. 28π / 3
tan θ = 0;cot θ = undef
; 112π / 3
25.
28. 0.3090
29. 0.9945
sin θ =
32.
2
35. 30 o
41.
47.
π
6
2
2
51. 24.9
3
3
26.
30. 2.6131
−2 13
− 13
;csc θ =
13
2
3 13
13
;sec θ =
13
3
tan θ = −2 / 3;cot θ = −3 / 2
42.
π
3
31.
3
1
sin θ = ;csc θ = 2
2
− 3
−2 3
34. cos θ =
;sec θ =
2
3
3
tan θ = −
;cot θ = − 3
3
33. cos θ =
36. 15 o
27. 2.6131
3
37. 20 o
38. 60 o
43. − 2
44. −
2
2
39. π / 4
45.
48. 2
49. − 3
50. -2
52. 0.5774
53. undefined
54. -1.0515
−2 3
3
40.
46.
π
3
3