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```Chapter 4 - 5 Exam Review
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
1) r = 4 inches, s = 8 inches
1
B) 2°
2
Convert the angle in degrees to radians. Express answer as a multiple of π.
2) 54°
4π
1
3π
A)
C)
11
5
10
2π
D)
9
Convert the angle in radians to degrees.
9
3)
π
10
A) 200π°
B) 160°
C) 324°
D) 162°
Convert the angle in radians to degrees. Round to two decimal places.
A) -0.1°
B) -495.44°
C) -0.15°
D) -495.61°
Find a positive angle less than 360° or 2π that is coterminal with the given angle.
6) 668°
A) 334°
B) 308°
C) 488°
D) 298°
16π
9
A)
2)
3)
Convert the angle in degrees to radians. Round to two decimal places.
4) 79°
7) -
1)
4)
5)
6)
7)
16π
9
B)
11π
9
C)
2π
9
D)
20π
9
Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places.
8) r = 45 inches, θ = 25°
8)
A) 19.63 inches
B) 20.92 inches
C) 17.78 inches
D) 22.06 inches
Solve the problem.
9) A pendulum swings through an angle of 25° each second. If the pendulum is 60 inches long, how
far does its tip move each second? If necessary, round the answer to two decimal places.
A) 26.18 inches
B) 27.47 inches
C) 24.33 inches
D) 28.61 inches
1
9)
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.
10) Find sec θ.
10)
2
3
A)
13
2
B)
2 13
3
C)
2 13
13
D)
3 13
13
Find a cofunction with the same value as the given expression.
π
11) sin
14
A) cos
π
14
12) cos 42°
A) csc 48°
B) cos
3π
7
11)
C) sin
B) sin 42°
π
14
C) sin 48°
D) sin
3π
7
D) sec 42°
Solve the problem.
13) A building 150 feet tall casts a 70 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) 64.98°
B) 28.87°
C) 61.13°
D) 64.23°
12)
13)
Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round your answer to
the nearest whole number.
14)
14)
a
29°
b = 19
A) a = 9 cm
B) a = 11 cm
C) a = 34 cm
D) a = 1 cm
A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ.
15) (3, -2) Find sin θ.
15)
2 13
3 13
13
A) B)
C) -2
D)
13
13
3
2
Find the exact value of the indicated trigonometric function of θ.
3
16) csc θ = - , θ in quadrant III
Find cot θ.
2
2 5
5
A) -
17) cos θ =
A) -
B)
4
, tan θ < 0
9
5
2
C) -
16)
5
3
D) -
3 5
5
Find sin θ.
9
4
17)
B) - 65
C) -
65
9
65
4
D) -
Use reference angles to find the exact value of the expression. Do not use a calculator.
-5π
18) tan
6
A)
3
2
B)
19) csc 1020°
2 3
A) 3
3
3
C) -
18)
3
D)
3
2
1
D) 2
19)
B) -
3
C) -
Find the exact value by using a sum or difference identity.
20) sin 105°
2( 3 - 1)
2( 3 + 1)
A) B)
4
4
20)
C) -
Find the exact value of the expression.
21) sin 255° cos 15° - cos 255° sin 15°
3
17
A)
B)
2
4
2( 3 + 1)
4
2( 3 - 1)
4
D)
21)
C) -
Find the exact value by using a difference identity.
22) tan 75°
A) 3 + 2
B) 3 - 2
3
2
D) -
1
2
22)
C) -
3+2
D) -
3-2
Use the figure to find the exact value of the trigonometric function.
23) Find tan 2θ.
17
15
240
A)
289
23)
8
B) -
161
289
C) -
3
240
161
D)
160
161
Use the given information to find the exact value of the expression.
5
24) tan θ =
, θ lies in quadrant III
Find sin 2θ.
12
A) -
119
169
B) -
120
169
C)
24)
119
169
D)
120
169
Write the expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression.
25) cos2 30° - sin2 30°
25)
A)
3
2
B) -
26) 2 sin 60° cos 60°
3
A)
2
1
2
C)
1
2
26)
B)
1
2
C) -
Use a half-angle formula to find the exact value of the expression.
27) cos 75°
1
1
1
A) 2- 3
B) 2+ 3
C)
2
2
2
28) sin
3
2
D) -
1
2
3
2
D) -
2-
3
1
D)
2
27)
2+
3
3π
8
A) -
28)
1
2
2+
2
B) -
1
2
2-
2
C)
1
2
2-
2
D)
1
2
Use the given information to find the exact value of the trigonometric function.
1
θ
29) cos θ = , csc θ > 0
Find sin .
4
2
A)
8 + 2 15
4
B)
8 - 2 15
4
C)
4
10
4
2+
2
29)
D)
6
4
Testname: CHAPTER 4-5 REVIEW-2017
1) C
2) C
3) D
4) C
5) D
6) B
7) C
8) A
9) A
10) A
11) B
12) C
13) D
14) B
15) A
16) B
17) C
18) B
19) A
20) B
21) C
22) A
23) C
24) D
25) C
26) A
27) C
28) D
29) D
5
```
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