S2 Exam Review Questions for your exam will be similar to the questions on this review.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. 1) Find sin θ. 1)
7
3 58 7
A)
58 3
B)
C)
7
58 58
D)
3
58 58
2) Find csc θ.
2)
8
5 A)
5
89 89
B)
8
89 89
89 5
C)
D)
89 8
3) Find cos θ.
3)
5
6 A)
61 5
B)
5
61 61
C)
1
6
61 61
D)
61 6
4) Find sec θ.
4)
5
2 A)
5
29 29
B)
5
29
29 5
C)
2
D)
2
29 29
5) Find tan θ.
5) 2
7
53 7
A)
B)
7 2
53 2
C)
D)
2 7
6) Find cot θ.
6) 8
7
A)
8 7
B)
7 8
C)
8
113 113
D)
7
θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value. 5 7) sin θ = , cos θ = 2 6 . Find csc θ. 7 7 A)
8) sin θ = A)
5
6 12
B)
7
6
C)
12
2
6 5
D)
6 12
B)
5
7)
7 5
5 , cos θ = 2 6 . Find tan θ. 7 7 5
113 113
8)
6
C)
5
2
7
6 12
D)
7 5
Use the given triangles to evaluate the expression. Rationalize all denominators.
9) cos 30°
9) 2
A)
B)
2
2
3
3
C)
3
D)
2
3
10) sin " 3
10) 3
A)
3
B)
3
C)
2
1 2
2
D)
2
11) csc " 3
11)
A) 2
B)
2
3
3
C)
3
D)
2
2
12) sec 60° - cos 30° A)
12)
3
-
B)
6
4- 3 2
C)
4- 2 2
D)
4
3-3 6
13) cot 60° - sin 45° A)
2
2-3 6
13) 3
B)
2
3-3 6
2
C)
2- 3 2
D)
2- 2 2
14) tan " - cos " 6 6 A) -
3 6
2
14) B)
2
3-3 6
2
C) -
3
6 2
D)
3
θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value. 3 15) sin θ = , cos θ = 2 10 . Find csc θ. 7 7 A)
16) sin θ = A)
7
10 20
2
5
B)
2
4
10
C)
3
3
10 20
D)
7 3
16)
7 2
C)
7
5
D)
15
2
5 15
7 , cos θ = 3 . Find sec θ. 4
7
B)
3
17)
4 3
C)
4
7
D)
7
3
7 7
7 , cos θ = 3 . Find cot θ. 4 4
18) sin θ = A)
2
2 , cos θ = 3 5 . Find tan θ. 7 7
17) sin θ = A)
B)
15)
7
-4 7
18)
7
B)
C)
3
7
-3 7
D)
4 3
Solve the problem. 19) A building 240 feet tall casts a 100 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 5 feet above ground level.) A) 67.38° B) 66.95° C) 25.18° D) 64.82° 20) A radio transmission tower is 130 feet tall. How long should a guy wire be if it is to be attached 10 feet from the top and is to make an angle of 21° with the ground? Give your answer to the nearest tenth of a foot. A) 128.5 feet B) 139.2 feet C) 362.8 feet D) 334.9 feet
19)
20)
A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ. 21) (9, 12) Find sin θ. 21) 3 4 4 3 A) B) C) D) 5 3 5 4 22) (3, 4) Find csc θ. 5 A) 3
22) 5 B) 4
3 C) 4
4
4 D) 3
23) (-5, 7) Find cot θ. 7 A) 5
23) 5 B) 9
7 C) 9
5 D) 7
The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the values of the indicated trigonometric function at t. 24)
5, 6
11 6 11 6
A)
25)
5, 8
39 8
A)
4
29)
A)
30)
11 11
39 5
C)
D)
5
39 39
3
55 55
C)
8 3
D)
8
55 55
Find cos t.
7
27) 7
7
C) -
3
4
D) - 4
7 7
21 5
3
7
7
C)
7
4
D)
3 4
Find tan t.
21 21
21 21
28) B)
3
5
5
Find sin t.
21 , 2 5 5 A)
39 8
B) -
2
D)
26) B)
3 4
3, 7 4 4
2, 5
5 6
Find sec t.
55 3
A)
C)
25) B)
7, 3 4
A)
11 5
B)
8 5
A)
27) -
24)
Find tan t.
55 , 3 8 8
26)
28)
Find sin t.
29) B)
21 5
21 2
C)
D)
5 2
Find sec t.
30) B)
21 2
C)
5
5 2
D)
2
21 21
31) -
55 , 3 8 8
Find cos t.
31)
55 8
A) -
B) -
55 3
C) - 8
55 55
D)
3 8
Use the unit circle to find the value of the trigonometric function. 32) cot " 6 A)
3
B) 1
3
32)
C)
3
3
D)
2
33) sec " 3 A)
33) 3
B) 2
2
C)
2
D)
2
3
34) sin 5" 6
3
A)
34) 3
B)
2
1 2
C)
2
3 3
D) 2
35) tan 3" 2
35)
A) 1
B) undefined
C) 0
D) -1
Solve the triangles in 36-41 using the Law of Sines. 36)
36)
80° 7
45° A) B = 55°, a = 6.04, c = 8.42 C) B = 55°, a = 8.42, c = 6.04
B) B = 60°, a = 6.04, c = 8.42 D) B = 50°, a = 8.42, c = 6.04
6
37)
37)
4 30°
125°
A) C = 20°, a = 3.38, c = 6.55 C) C = 25°, a = 3.38, c = 6.55
B) C = 30°, a = 6.55, c = 3.38 D) C = 25°, a = 6.55, c = 3.38
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 38) B = 50° C = 111° b = 48 A) A = 17°, a = 58.5, c = 20.4 B) A = 19°, a = 22.4, c = 60.5 C) A = 17°, a = 60.5, c = 22.4 D) A = 19°, a = 20.4, c = 58.5 39) A = 47° B = 33° a = 37.4 A) C = 101°, b = 50.4, c = 27.9 C) C = 100°, b = 50.4, c = 27.9
B) C = 100°, b = 27.9, c = 50.4 D) C = 101°, b = 27.9, c = 50.4
40) A = 26°, B = 51°, c = 27 A) C = 103°, a = 12.1, b = 21.5 C) C = 103°, a = 21.5, b = 12.1
B) C = 97°, a = 11.9, b = 21.1 D) C = 103°, a = 60, b = 33.9
41) A = 11.2°, C = 131.6°, a = 86.8 A) B = 37.2°, b = 334.2, c = 270.2 C) B = 37.2°, b = 270.2, c = 334.2
B) B = 37.2°, b = 27.9, c = 22.6 D) B = 36.8°, b = 267.7, c = 334.2
38)
39)
40)
41)
Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 42) A = 30°, a = 13, b = 26 42) A) B = 60°, C = 90°, c = 22.5 B) B = 90°, C = 60°, c = 22.5 C) no triangle D) B = 60°, C = 60°, c = 22.5 43) B = 82°, b = 5, a = 25 A) A = 41°, C = 57°, c = 30 C) A = 42°, C = 57°, c = 34
B) A = 40°, C = 57°, c = 32 D) no triangle
43)
44) B = 75°, b = 4, c = 5 A) C = 39°, A = 66°, a = 13 C) C = 37°, A = 68°, a = 11
B) B = 38°, A = 67°, a = 9 D) no triangle
44)
7
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 45)
6
45)
4
7 A) A = 59°, B = 86°, C = 35° C) A = 35°, B = 86°, C = 59°
B) A = 59°, B = 35°, C = 86° D) A = 35°, B = 59°, C = 86°
46)
46)
8 5 4 A) A = 31°, B = 125°, C = 24° C) A = 125°, B = 24°, C = 31°
B) A = 31°, B = 24°, C = 125° D) A = 125°, B = 31°, C = 24°
47) a = 7, b = 9, C = 114° A) c = 16.4, A = 30°, B = 36° C) c = 19.3, A = 26°, B = 40°
47) B) c = 13.5, A = 28°, B = 38° D) no triangle
48) a = 6, c = 9, B = 122° A) b = 19, A = 21°, C = 37° C) b = 13.2, A = 23°, C = 35°
B) b = 16.1, A = 25°, C = 33° D) no triangle
49) b = 5, c = 12, A = 110° A) a = 17.4, B = 21°, C = 49° C) a = 20.3, B = 17°, C = 53°
B) a = 14.5, B = 19°, C = 51° D) no triangle
50) b = 2, c = 3, A = 70° A) a = 2, B = 71°, C = 39° C) a = 4, B = 39°, C = 71°
B) a = 3, B = 71°, C = 39° D) a = 3, B = 39°, C = 71°
48)
49)
50)
51) a = 8, c = 7, B = 90° A) b = 11.6, A = 49°, C = 41° C) b = 10.6, A = 41°, C = 49°
51) B) b = 10.6, A = 49°, C = 41° D) b = 9.6, A = 41°, C = 49°
52) a = 6, b = 14, c = 15 A) A = 22°, B = 72°, C = 86° C) A = 26°, B = 70°, C = 84°
B) A = 24°, B = 72°, C = 84° D) no triangle
52)
8
53) a = 5, b = 5, c = 2 A) A = 78°, B = 24°, C = 78° C) A = 78°, B = 78°, C = 24°
B) A = 24°, B = 78°, C = 78° D) A = 79°, B = 79°, C = 22°
53)
54) a = 9, b = 6, c = 5 A) A = 109°, B = 39°, C = 32° C) A = 39°, B = 32°, C = 109°
B) A = 109°, B = 32°, C = 39° D) A = 39°, B = 109°, C = 32°
54)
9
Answer Key Testname: S2EXAMREV
1) C 2) C 3) C 4) C 5) D 6) B 7) D 8) A 9) C 10) B 11) B 12) B 13) B 14) A 15) D 16) D 17) B 18) C 19) B 20) D 21) C 22) B 23) D 24) A 25) C 26) D 27) C 28) C 29) C 30) A 31) A 32) C 33) B 34) B 35) B 36) A 37) D 38) D 39) B 40) A 41) C 42) B 43) D 44) D 45) B 46) D 47) B 48) C 49) B 10
Answer Key Testname: S2EXAMREV
50) D 51) B 52) B 53) C 54) A
11
