AnswersAlgebra 2 MP 234 CHSChanges in Period and Phase Shift of Sine and Cosine Functions

Changes in Period and Phase Shift of Sine and Cosine Functions — Unit test Answers

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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
2
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Consider the relationship below, given .Which of the following best explains how this relationship and the value of sin can be used to find the other trigonometric values?

Question illustration
A
The values of sin and cos represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option A
B
The values of sin and cos represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
Option B
C
The values of sin and cos represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1, which can then be used to find all other values.
Option C
D
The values of sin and cos represent the legs of a right triangle with a hypotenuse of –1, since is in Quadrant II; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option D
3

The point P(x, y) is on the terminal ray of angle . If is between radians and radians and csc = , what are the coordinates of P(x, y)?

Question illustration
A
P(, –2)
Option A
B
P (, –2)
Option B
C
P(–2, )
Option C
D
P(–2, )
Option D
4

Which of the following could be the equation of the function below?

Question illustration
A
y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2
Option A
B
y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2
Option B
C
y = 0.5 cosine (4 (x + pi)) + 2
Option C
D
y = 0.5 cosine (2 (x minus pi)) minus 2
Option D
5

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

Question illustration
A
–180°
B
–120°
C
140°
D
510°
6

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
7

What is the range of y = –3sin(x) – 4?

A
all real numbers
Option A
B
all real numbers
Option B
C
all real numbers
Option C
D
all real numbers
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

What is the equation of the graph below?

Question illustration
A
y = sine (x + 90 degrees)
Option A
B
y = cosine (x + 90 degrees)
Option B
C
y = sine (x + 45 degrees)
Option C
D
y = cosine (x + 45 degrees)
Option D
10

Which is the graph of y = cos(x) + 3?

A
On a coordinate plane, a cosine curve has a maximum of 3 and a minimum of negative 3.
Option A
B
On a coordinate plane, a cosine curve has a maximum of 4 and a minimum of negative 2.
Option B
C
On a coordinate plane, a cosine curve has a maximum of negative 2 and a minimum of negative 4.
Option C
D
On a coordinate plane, a cosine curve has a maximum of 6 and a minimum of negative 0.
Option D
11

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.
12

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
13

Which of the following could be the equation of the function below?

Question illustration
A
y = negative 3 sine (2 (x + pi)) + 2
Option A
B
y = negative 3 sine (x + pi) + 2
Option B
C
y = 3 sine (4 (x minus pi)) + 4
Option C
D
y = 3 sine (2 (x + pi)) + 2
Option D
14

Which function describes the graph below?

Question illustration
A
f (x) = 6 cosine (x)
Option A
B
f (x) = 3 cosine (x) + 3
Option B
C
f (x) = 6 sine (x)
Option C
D
f (x) = 3 sine (x) + 3
Option D
15

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°
16

If , which of the following represents approximate values of and , for ?

Question illustration
A
sine theta almost-equals 0.9511; tangent theta almost equals 0.3249
Option A
B
sine theta almost-equals 0.9511; tangent theta almost equals 3.0780
Option B
C
sine theta almost-equals 3.2362; tangent theta almost-equals 0.0955
Option C
D
sine theta almost-equals 3.2362; tangent theta almost-equals 10.4731
Option D
17

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
18

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
19

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
20

Which of the following is the graph of y = cos(2x)?

A
mc008-1.jpg
Option A
B
mc008-2.jpg
Option B
C
mc008-3.jpg
Option C
D
mc008-4.jpg
Option D

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