Download Chapter 5 Practice Test review_5

Pre-Calculus Honors Chapter 5 Review
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use basic identities to simplify the expression.
tan θ
1)
cot θ
B) cos3 θ
A) sin θ
2)
C) tan2 θ
D) sec2 θ
1
+ sec θ cos θ
cot2 θ
A) csc2 θ
3) cot θ sec θ sin θ
A) sec2 θ
Simplify the expression.
4) sec (- x) cos (- x)
A) cot x
5) csc
2)
B) 1
C) sec2 θ
D) tan2 θ
B) csc2 θ
C) tan2 θ
D) 1
B) -1
C) - tan x
D) 1
3)
4)
π
- x cos (-x)
2
5)
B) -csc2 x
A) 1
6)
1)
D) cos2 x
C) -1
1 - sin2 x
sin x - csc x
6)
B) cos2 x
A) -cos x
D) sin 2 x
C) -sin x
Find all solutions in the interval [0, 2π).
7) sin2 x + sin x = 0
7)
4π 5π
A) x = 0, π,
,
3 3
C) x = 0, π,
3π
B) x = 0, π,
2
π 2π
,
3 3
8) 4 sin 2 x - 4 sin x + 1 = 0
π 5π
A) ,
3 3
D) x = 0, π,
π 5π
,
3 3
8)
B)
π 5π
,
6 6
C)
Find all solutions to the equation in the interval [0, 2π).
9) cos 2x - cos x = 0
π 7π 11π
2π 4π
A) 0, ,
,
B) 0,
,
2 6
6
3 3
7π 11π
,
6
6
D)
π 11π
,
6 6
9)
π 5π 3π
C) ,
,
6 6 2
1
D) No solution
10) cos x = sin 2x
π 3π
A) ,
2 2
10)
π π 5π 3π
B) , ,
,
6 2 6
2
π 5π
D) 0, ,
,π
6 6
C) 0, π
Find all solutions to the equation.
1
11) cos x = (Express your answer in radians, in exact form.)
2
A)
5π
7π
+ 2nπ ,
+ 2nπ | n = 0, ±1, ±2, ....
6
6
B)
2π
+ nπ | n = 0, ±1, ±2, ....
3
C)
2π
4π
+ 2nπ ,
+ 2nπ | n = 0, ±1, ±2, ....
3
3
D)
5π
+ nπ | n = 0, ±1, ±2, ....
6
Rewrite with only sin x and cos x.
12) cos 2x - sin x
A) cos2 x - 3 sin x
11)
12)
B) cos2 x - sin2 x - sin x
D) cos2 x - sin3 x
C) cos2 x + sin2 x + sin x
13) sin 2x - cos x
13)
A) cos x (2 sin x - 1)
B) 2 sin x cos2 x
C) sin x
D) 2 sin x
State whether the given measurements determine zero, one, or two triangles.
14) A = 77°, a = 26, b = 52
A) Two
B) One
14)
C) Zero
15) C = 44°, a = 22, c = 19
A) Zero
B) Two
C) One
15)
16) C = 31°, a = 32, c = 35
A) Zero
B) Two
C) One
16)
Solve.
17) A ranger in fire tower A spots a fire at a direction of 40°. A ranger in fire tower B, which is 28 miles
directly east of tower A, spots the same fire at a direction of 116°. How far from tower A is the fire?
A) 22 miles
B) 33 miles
C) 24 miles
D) 26 miles
Two triangles can be formed using the given measurements. Solve both triangles.
18) C = 72°, a = 27, c = 26
A) A = 9°, B = 99°, b = 25; A = 171°, B = 81°, b = 25
B) A = 81°, B = 27°, b = 12.4; A = 99°, B = 9°, b = 4.3
C) A = 81°, B = 27°, b = 54.5; A = 99°, B = 9°, b = 54.5
D) A = 9°, B = 99°, b = 27; A = 171°, B = 81°, b = 27
2
17)
18)
19) B = 32°, b = 27, c = 32
A) A = 109.1°, C = 38.9°, a = 15.1; A = 6.9°, C = 141.1°, a = 15.1
B) A = 109.1°, C = 38.9°, a = 48.1; A = 6.9°, C = 141.1°, a = 6.1
C) A = 96.9°, C = 51.1°, a = 50.6; A = 83.1°, C = 128.9°, a = 50.6
D) A = 96.9°, C = 51.1°, a = 14.4; A = 83.1°, C = 128.9°, a = 14.4
19)
Use the fundamental identities to find the value of the trigonometric function.
17
20) Find tan θ if sec θ =
and sin θ < 0.
4
A) - 4
B) 4
C) -
21) Find sin θ if tan θ = -
5
and cos θ > 0.
12
13
5
B) -
A) -
1
4
20)
D) -
17
21)
5
13
C)
Solve the triangle.
22) a = 3.5, b = 7.8, c = 6.5
A) No triangles possible
C) A ≈ 26.4°, B ≈ 98°, C ≈ 55.6°
12
13
D) -
12
13
22)
B) A ≈ 26.4°, B ≈ 55.6°, C ≈ 98°
D) A ≈ 26.4°, B ≈ 101°, C ≈ 52.6°
Find the area. Round your answer to the nearest hundredth if necessary.
23) Find the area of the triangle with the following measurements:
C = 108°, a = 1.7 in., b = 4.9 in.
A) 3.96 in. 2
B) 4.165 in. 2
C) 7.92 in. 2
23)
D) 1.29 in. 2
Decide whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the
triangle.
24) a = 14
24)
b=5
c=7
A) 24.00
B) 25.92
C) No triangle is formed.
D) 24.98
25) a = 19.1
b = 11.3
c = 14.7
A) No triangle is formed.
C) 85.89
25)
B) 91.89
D) 82.89
Solve the problem.
26) To find the distance between two small towns, an electronic distance measuring (EDM) instrument
is placed on a hill from which both towns are visible. If the distance from the EDM to the towns is
4.1 miles and 4.5 miles and the angle between the two lines of sight is 37°, what is the distance
between the towns? Round your answer to the nearest tenth of a mile.
A) 8.2 miles
B) 7.2 miles
C) 4.7 miles
D) 2.8 miles
3
26)
Answer Key
Testname: REVIEW 5
1) C
2) C
3) D
4) D
5) A
6) C
7) B
8) B
9) B
10) B
11) C
12) B
13) A
14) C
15) B
16) C
17) D
18) B
19) B
20) C
21) B
22) C
23) A
24) C
25) D
26) D
4