AnswersAlgebra 2 MP 234 CHSThe Unit Circle

The Unit Circle — Unit test Answers

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1
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What is the approximate length of arc s on the circle below? Use 3.14 for . Round your answer to the nearest tenth.

Question illustration
A
14.1 in.
B
22.5 in.
C
42.3 in.
D
56.5 in.
2
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An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth.

A
0.4 radian
B
1.0 radian
C
2.7 radians
D
5.0 radians
3

Angle D has a measure between 0° and 360° and is coterminal with a –920° angle. What is the measure of angle D?

A
155°
B
160°
C
165°
D
170°
4

An angle measuring (468n)° is in standard position. For which value of n will the terminal side fall on the x-axis?

A
n = 4
B
n = 5
C
n = 6
D
n = 7
5

Which of the following best explains the value of on the unit circle below?

Question illustration
A
The length opposite the angle is the vertical distance from the x-axis on the graph.
Option A
B
The length adjacent to the angle is the vertical distance from the x-axis on the graph.
Option B
C
The length opposite the angle is the horizontal distance from the y-axis on the graph.
Option C
D
The length adjacent to the angle is the horizontal distance from the y-axis on the graph.
Option D
6

What are the values of m and in the diagram below?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
7

Which of the following is true of the location of an angle, , whose tangent value is ?

Question illustration
A
has a 30-degree reference angle and is located in Quadrant II or IV
Option A
B
has a 30-degree reference angle and is located in Quadrant II or III
Option B
C
has a 60-degree reference angle and is located in Quadrant II or IV
Option C
D
has a 60-degree reference angle and is located in Quadrant II or III
Option D
8

The angle measures associated with which set of ordered pairs share the same reference angle?

A
(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option B
C
(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
9

Which of the following are in the correct order from least to greatest?

A
, , 80°, , 38°
Option A
B
38°, 80°, , ,
Option B
C
38°, , 80°, ,
Option C
D
, 38°, 80°, ,
Option D
10

What is 270° converted to radians?

A
StartFraction pi Over 6 EndFraction
Option A
B
StartFraction 3 Over 2 EndFraction
Option B
C
StartFraction 3 pi Over 2 EndFraction
Option C
D
3
11

Which of the following could be the measure of the angle below?

Question illustration
A
–180°
B
–120°
C
140°
D
510°
12

Which of the following represents the measures of all angles coterminal with a 418° angle?

A
360 + 58n, for any whole number n
B
58 + 360n, for any integer n
C
58 + 360n, for any whole number n
D
360 + 58n, for any integer n
13

Which expression is equivalent to ?

Question illustration
A
sine StartFraction pi Over 6 EndFraction
Option A
B
sine StartFraction 5 pi over 3 EndFraction
Option B
C
sine StartFraction 5 pi over 3 EndFraction
Option C
D
sine StartFraction 11 pi Over 6 EndFraction
Option D
14

What is the value of in the diagram below?

Question illustration
A
Three-fifths
Option A
B
Three-fourths
Option B
C
Four-fifths
Option C
D
Four-thirds
Option D
15

Which measure is of an angle that is coterminal with a 135° angle?

A
45°
B
90°
C
495°
D
585°
16

A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measure of the central angle, q?

A
Theta= five-sevenths
Option A
B
Theta = Seven-fifths
Option B
C
Theta = 7 + 5
Option C
D
Theta = 7 times 5
Option D
17

Which expression converts 8 radians to degrees?

A
8 times pi
Option A
B
8 times StartFraction pi Over 180 degrees EndFraction
Option B
C
8 times 180 degrees
Option C
D
8 times StartFraction 180 degrees Over pi EndFraction
Option D
18

How long is the arc intersected by a central angle of radians in a circle with a radius of 4.5 cm? Round your answer to the nearest tenth. Use 3.14 for .

Question illustration
A
0.3 cm
B
0.7 cm
C
2.9 cm
D
7.1 cm
19

Which angle has a positive measure?

A
On a coordinate plane, a ray moves counter-clockwise to form an angle.
Option A
B
On a coordinate plane, a ray moves clockwise to form an angle.
Option B
C
On a coordinate plane, a ray moves clockwise to form an angle.
Option C
D
On a coordinate plane, a ray moves clockwise to form an angle.
Option D
20

Which expression can be used to determine the reference angle for an angle, x, measuring 150°?

A
180 degrees minus x
Option A
B
x minus 180 degrees
Option B
C
360 degrees minus x
Option C
D
x minus 360 degrees
Option D

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