Rich – AAT (H)
Name: _________________________________
Review Unit 3 Part A Test Trig & The Unit Circle
Date: ____________________ Period: ________
#1 – 10: Multiple choice. Write the letter for the correct answer on the blank to the left of each question.
LT 3.A.1: evaluate trigonometric functions of acute angles (including special right triangles); LT 3.A.2: use the fundamental
trigonometric identities; LT 3.A.3: use a calculator to evaluate trigonometric functions.
______ 1. Find the value of csc A .
8
17
A.
B.
17
15
17
C.
8
C
B
8
17
15
D.
17
A
______ 2. Which equation can be used to find x?
A. sin21 
8
x
8
C. tan21 
x
B. tan21 
8
x
x
8
21°
x
D. sin21 
8
A
______ 3. Find A to the nearest degree.
A. 49
B. 37
C. 41
D. 53
29
C
25
B
LT 3.A.17: convert between degree and radian measures.
______ 4. Rewrite
2
radians in degree measure.
9
A. 20
B. 80
C. 40
LT 3.A.15: find coterminal angles.
D.
40

5
?
9
10
D.
9
______ 5. Which angle is coterminal with an angle in standard position measuring 
A.
13
9
B.
5
9
C.
23
9
LT 3.A.8: find all trigonometric values of a function with given constraints.
______ 6. Find the exact value of sin if the terminal side of θ in standard position contains the point
(-4, -3).
A. 
4
5
B. 
3
5
C.
3
5
D.
4
5
LT 3.A.19: use the unit circle to identify trig functions of angles. LT 3.A.6: use reference angles to evaluate trigonometric
functions; LT 3.A.7: determine the quadrant of an angle based on the sign of the given trigonometric function.
______ 7. Find the exact value of cot450 .
A. 0
B. undefined
C. 1
D. -1
 
______ 8. Find the exact value of cos    .
 4
A.
2
2
B. 
2
2
C.
3
2
D. 
3
2
LT 3.A.9: use the Law of Sines to solve oblique triangles, including the ambiguous case.
______ 9. In ∆ABC, A = 40°, B = 60°, and a = 5. Find b.
A. 6.4
B. 7.5
C. 6.7
D. 3.7
LT 3.A.10: find the areas of oblique triangles.
______ 10. Find the area of ∆ABC if A = 72°, b = 9 feet and c = 10 feet.
A. 85.6 ft2
B. 42.8 ft2
C. 45.0 ft2
D. 13.9 ft2
LT 3.A.6: use reference angles to evaluate trigonometric functions; LT 3.A.7: determine the quadrant of an angle based on the
sign of the given trigonometric function; LT 3.A.14: sketch and describe angles; LT 3.A.18: use degree and radian measures;
#11 – 14: Draw an angle with the given measure in standard position. Then, state the reference angle θ’.
11. 710°
11.  '  _________
12. -120°
12.  '  _________
13.
11
6
13.  '  _________
14. 
10
3
14.  '  _________
LT 3.A.7: determine the quadrant of an angle based on the sign of the given trigonometric function; LT 3.A.14: sketch and
describe angles; LT 3.A.18: use degree and radian measures.
#15 – 18: State the quadrant in which the terminal side of each angle lies.
5
15. 509°
16. 
17. -340°
6
15. ___________
16. ___________
18.
17. ___________
5
3
18. ___________
LT 3.A.8: find all trigonometric values of a function with given constraints.
#19 – 24: Find the exact values of the 6 trigonometric functions of  given each coordinate point.
19. (13, 9)
20. (-4, 16)
21. (4, -6)
22. (-2,  5 )
23. ( 17 , -8)
24. (16, 16)
LT 3.A.15: find coterminal angles.
#25 – 27: Determine if the given angles are coterminal to each other. Circle YES or NO.
17 161
,
25. 240°, 600°
26. 185°, -545°
27.
36
36
YES
NO
YES
NO
YES
NO
LT 3.A.15: find coterminal angles; LT 3.A.18: use degree and radian measures.
#28 – 31: Find a coterminal angle for θ between 0° and 360°, or between 0 and 2π radians depending on
the unit of measure of θ.
11
15
28. θ = -330°
29. θ = 640°
30. θ =
31. θ =
3
4
28. ___________
29. ___________
30. ___________
31. ___________
LT 3.A.6: use reference angles to evaluate trigonometric functions; LT 3.A.7: determine the quadrant of an angle based on the
sign of the given trigonometric function; LT 3.A.15: find coterminal angles; LT 3.A.17: convert between degree and radian
measures; LT 3.A.18: use degree and radian measures.
#32 – 34: Find one positive and one negative coterminal angle for each given angle. Then, state the
reference angle for each given angle and convert the original angle to degrees.
32.
5
4
33. 
7
6
34.
7
9
32. pos: ____________
33. pos: ____________
34. pos: ____________
neg: ____________
neg: ____________
neg: ____________
θ’=_____________
θ’=_____________
θ’=_____________
degrees: ________
degrees: ________
degrees: ________
LT 3.A.19: use the unit circle to identify trig functions of angles.
#35 – 39: Find the exact values of each trig function.
 11 
35. csc(-270°)
36. sec 
37. tan(480°)

 3 
35. ______
36. ______
37. ______
 9 
38. cot 

 4 
38. ______
 10 
39. sin  

 3 
39. ______
LT 3.A.3: use a calculator to evaluate trigonometric functions; LT 3.A.4: use trigonometric functions to model and solve real-life
problems; 3.A.5: evaluate trigonometric functions of any angle; LT 3.A.11: use Law of Sines to model and solve real-life problems;
LT 3.A.13: use Law of Cosines to model and solve real-life problems; LT 3.A.20: use angles to model and solve real-life problems.
#40 – 43: Complete the following application problems.
40. A tree is observed on the opposite bank of a river. At that point, the river is known to be 140 feet wide.
The angle of elevation from a point 5 feet off the ground to the top of the tree is 20°. Find the height of
the tree to the nearest foot.
40. _______________________
41. A private plane flies 1.3 hours at 110 mph and an angle of 40° east of due north (heading northeast).
Then it turns and continues another 1.5 hours at the same speed, but at an angle of 50° east of due
south (now headed south east). At the end of this time, how far is the plane from its starting point to
the nearest mile?
41. _______________________
42. The angle of depression from an airplane to the base of GNHS is 23° while the angle of depression to
the base of GCHS is 42°. If GNHS and GCHS are 3 miles apart, what is the horizontal distance between
the airplane and GNHS? Round to the nearest tenth.
42. _______________________
43. The angle of elevation from a luxury yacht to a lighthouse is 56 o. The yacht drifts out another ¼ mile,
where the angle of elevation is now 42o. How tall is the lighthouse to the nearest foot?
43. _______________________
LT 3.A.10: find the areas of oblique triangles.
#44 – 47: Find the area of each triangle to the nearest tenth.
44. D = 99°, e = 11 cm, f = 11 cm
44. Area = _______________
46. P = 36°, k = 7 mi, h = 4 mi
46. Area = _______________
45. R = 28°, p = 7.6 km, q = 6.7 km
45. Area = _______________
47. X = 50°, y = 5 mi, z = 12 mi
47. Area = _______________
LT 3.A.9: use the Law of Sines to solve oblique triangles, including the ambiguous case; LT 3.A.12: use the Law of Cosines to solve
oblique triangles.
#48 – 52: Determine whether each triangle has no solution, one solution, or two solutions. State whether
each triangle should be solved by beginning with the Law of Sines or Law of Cosines. Then solve
each triangle. Round angles to the nearest degree and sides to the nearest tenth.
48. A = 58°, a = 17, b = 12
48. # of Solutions: ___________________
Begin with Law of ________________
B = ______
B’ = _____
C = ______
C’ = _____
c = ______
c’ = _____
49. A = 110°, a = 6, b = 15
49. # of Solutions: ___________________
Begin with Law of ________________
B = ______
B’ = _____
C = ______
C’ = _____
c = ______
c’ = _____
50. A = 70°, a = 9, c = 26
50. # of Solutions: ___________________
Begin with Law of ________________
B = ______
B’ = _____
C = ______
C’ = _____
b = ______
b’ = _____
51. C = 114.6°, a = 5, b = 7
51. # of Solutions: ___________________
Begin with Law of ________________
A’ = _____
B = ______
B’ = _____
c = ______
c’ = _____
C
52.
18
10.4
B
A = ______
21.9
52. # of Solutions: ___________________
A
Begin with Law of ________________
A = ______
A’ = _____
B = ______
B’ = _____
C = ______
C’ = _____
*** Know your vocab, Unit Circle (blank one on back), and all formulas from this unit ***
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