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Test 2 (A) Math 1316
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the triangle with the given parts.
1)
1)
26 B) γ = 103°, a = 20.7, b = 11.7
D) γ = 103°, a = 11.7, b = 20.7
A) γ = 97°, a = 11.5, b = 20.4
C) γ = 103°, a = 57.8, b = 32.6
Solve the triangle. If there is more than one triangle with the given parts, give both solutions.
2) β = 58.3°
b = 4.47
a = 22.6
A) No solution
B) α = 30.15°, γ = 92.55°, c = 31.07
D) α = 28.15°, γ = 92.55°, c = 29.07
C) α = 29.15°, γ = 92.55°, c = 27.07
2)
3)
3) β = 16.6°
b = 9.52
a = 18.9
A) α = 7.3°, γ = 155.1°, c = 30.4
B) α = 9.3°, γ = 155.1°, c = 31.4
D) α = 8.3°, γ = 155.1°, c = 28.4
C) α = 34.6°, γ = 128.8°, c = 26.0
αʹ = 145.4°, γʹ = 18.0°, cʹ = 10.3
Solve the triangle with the given information.
4) a = 8.5
b = 13.2
c = 15.0
A) α = 36.3°, β = 59.2°, γ = 84.5°
C) α = 32.3°, β = 61.2°, γ = 86.5°
4)
B) α = 34.3°, β = 61.2°, γ = 84.5°
D) No solution
5)
5) β = 63.5°
a = 12.20
c = 7.80
A) b = 12.2, α = 75.1°, γ = 41.4°
C) b = 13.2, α = 73.1°, γ = 37.4°
B) b = 11.2, α = 77.6°, γ = 38.9°
D) No solution
1
Find the area of triangle ABC.
6) α = 22.7°
b = 12.0
c = 6.9
A) 16
6)
B) 40.2
C) 38.2
Find the area of the triangle using Heronʹs formula. Round to the nearest unit.
7) a = 13.4
b = 13.4
c = 15.5
A) 85
B) 94
C) 91
D) 14
7)
D) 88
Solve the problem.
8) A tower is supported by a guy wire 483 ft long. If the wire makes an angle of 34° with respect to
the ground and the distance from the point where the wire is attached to the ground and the tower
is 201 ft, how tall is the tower? Round your answer to the nearest tenth.
A) 659.3 ft
B) 439.6 ft
C) 335.7 ft
D) 595.1 ft
9) Two tracking stations are on the equator 123 miles apart. A weather balloon is located on a bearing
of N 32°E from the western station and on a bearing of N 18°E from the eastern station. How far is
the balloon from the western station? Round to the nearest mile.
D) 493 mi
A) 380 mi
B) 389 mi
C) 484 mi
Find all real numbers in the interval [0, 2 π) that satisfy the equation.
10) cos2 x + 2 cos x + 1 = 0
π 7π
A)
, 4 4
11) sin2 x + sin x = 0
π 2π
A) 0, π, , 3 3
π 3π
, 2 2
8)
9)
10)
B) {π}
C)
D) {2π}
4π 5π
B) 0, π, , 3
3
π 5π
C) 0, π, , 3 3
3π
D) 0, π, 2
π 5π
C) , 3 3
3π
D)
2
11)
Find all real numbers in [0, 2π] that satisfy the equation.
12) 2 cos x + 1 = 0
π 3π
2π 4π
A) , B)
, 2 2
3
3
12)
Find all real numbers that satisfy the equation.
3
13) sin x = - 2
13)
π
2π
A) {x|x = - + 2kπ, x = - + 2kπ}
3
3
π
5π
B) {x|x = + kπ, x = + kπ}
6
6
2π
π
+ kπ}
C) {x|x = + kπ, x = 3
3
π
5π
D) {x|x = + 2kπ, x = + 2kπ}
6
6
2
Find the exact value of the expression without using a calculator or table.
3
14) cos-1 2
A)
11π
6
B)
π
4
C)
π
6
14)
D)
7π
4
Find the exact value of the composition.
1
5
15) cos arcsin 2
13
A)
3 13
13
B)
15)
26
26
C)
2 13
13
D)
5 26
26
Write the expression in terms of sines and/or cosines, and then simplify.
tan x
16)
sec x
A)
1 + sin2 x cos2 x
cos2 x
B) sin x
C)
1 + sin x cos x
cos x
D)
16)
1 + cos2 x
cos2 x
Use identities to find the exact value of the function for the given value.
2
17) cos α = and α is in quadrant IV; Find sin α.
3
A)
3 7
7
B)
5
4
C) - 5
3
17)
D) - 3
2
Factor and simplify the expression.
sin2 x - 1
18)
sin x + 1
A) sin x
18)
B) cos2 x
C) sin x - 1
Find the exact value by using a sum or difference identity.
19) cos 75°
2( 3 + 1)
2( 3 - 1)
B) - A)
4
4
D) sin x + 1
19)
2( 3 + 1)
4
C)
D) - Use the sum/difference identities to simplify the expression. Do not use a calculator.
7π
5π
7π
5π
20) cos cos + sin sin 12
12
12
12
A)
3
2
B) - 1
C)
3
1
2
2( 3 - 1)
4
20)
D)
2
2
Find cos(A + B).
1
1
π
π
21) cos A = and sin B = , where 0 < A < and < B < π.
3
4
2
2
15 + 2 2
12
A) - 15 - 2 2
12
B)
21)
15 - 2 2
6
C)
15 + 2 2
6
D) - Use the identities for the cosine of a sum or a difference to write the expression as a single function of α.
22) cos (α + 90°)
A) cos α
B) -cos α
C) -sin α
D) sin α
Find the exact value by using a sum or difference identity.
7π
23) sin 12
2 - 6
4
A)
23)
2 + 6
4
B)
22)
2 + 2 6
4
C)
Use trigonometric identities to find the exact value.
24) sin 20° cos 100° + cos 20° sin 100°
3
3
A) - B)
2
2
6 - 2
4
D)
24)
1
C)
3
1
D) - 2
Solve the problem.
1
1
25) If cos A = and sin B = - , with A in quadrant I and B in quadrant IV, then find sin(A - B).
3
2
A)
2 6 + 1
6
3 + 2 2
6
B)
3 - 2 2
6
C)
D)
2 6 - 1
6
Find the exact value using a double -angle identity.
5π
26) cos 3
A)
1
2
B) - 26)
3
2
C) 0
D) - 3
Find the exact value by using a half-angle identity.
π
27) sin 12
A)
1
1 + 3
2
B)
25)
27)
1
1 - 3
2
C)
1
2 - 3
2
D)
1
2 + 3
2
Solve the problem.
28) Find sin 2θ. tan θ = A) - 527
625
7
, θ lies in quadrant III.
24
B)
28)
336
625
C)
4
527
625
D) - 336
625
29)
29)
5
4
3
Find the exact value of cos 2θ.
7
7
A)
B) - 25
25
C) - 1
5
D)
24
25
Use the given information given to find the exact value of the trigonometric function.
3
θ
30) cos θ = - ,
θ lies in quadrant III
Find cos .
5
2
A) - 5
5
B)
30
10
C)
5
5
Use a product-to-sum identity to rewrite the expression.
31) sin 33° cos 2°
A) 0.5(cos(31°) - cos(35°))
C) 0.5(cos(35°) + cos(31°))
B) 0.5(sin(35°) + sin(31°))
D) 0.5(sin(31°) - sin(35°))
Use a sum-to-product identity to rewrite the expression.
32) cos 75° + cos 60°
A) 2(sin (67.5°) sin (7.5°))
C) 2(sin (7.5°) cos (67.5°))
B) 2(cos (67.5°) cos (7.5°))
D) 2(sin (67.5°) cos (7.5°))
Find the exact value of the sum.
33) cos 75° - cos 15°
2
A)
2
3
C)
2
30)
D) - 30
10
31)
32)
33)
1
B)
2
5
2
D) - 2
Answer Key
Testname: TEST 2 (A) MATH 1316 SUM 2012
1) D
2) A
3) C
4) B
5) B
6) A
7) A
8) C
9) C
10) B
11) D
12) B
13) A
14) C
15) D
16) B
17) C
18) C
19) A
20) A
21) A
22) C
23) B
24) B
25) A
26) A
27) C
28) B
29) B
30) A
31) B
32) D
33) D
6