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 statement accurately describes how adding a number, n, to the function affects its graph?

Question illustration
A
There is a vertical shift of n units.
B
The x-intercepts will shift n units.
C
There is a change in amplitude of n units.
D
The range will change by a factor of 2n units.
2
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An angle that shares the same sine value of an angle that measures radians is located where?

Question illustration
A
Quadrant I
B
Quadrant II
C
Quadrant IV
D
along an axis
3

In the triangle below, angle B measures 60° and BC is 18. What is the length of AC?

Question illustration
A
9 StartRoot 3 EndRoot
Option A
B
StartFraction 9 Over StartRoot 3 EndRoot EndFraction
Option B
C
9
D
StartFraction StartRoot 3 EndRoot Over 9 EndFraction
Option D
4

Which formula gives the zeros of y = sin(x)?

A
for any positive integer k
Option A
B
for any integer k
Option B
C
for any positive integer k
Option C
D
for any integer k
Option D
5

Melanie simplified the expression as shown below.Step 1:Step 2:Step 3:Step 4:In which step did Melanie make the first error, and which expression should she have written in that step?

Question illustration
A
step 1;
Option A
B
step 1;
Option B
C
step 4; cos(x)
D
step 4; csc(x)
6

What is the length of the hypotenuse in the triangle below?

Question illustration
A
14 cm
B
cm
Option B
C
cm
Option C
D
28 cm
7

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . What is the height of the ball at its equilibrium?

Question illustration
A
a feet
B
b feet
C
h feet
D
k feet
8

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at pi.
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 1 cycle at 2 pi.
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option D
9

Which function is the same as ?

Question illustration
A
y = 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option A
B
y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option B
C
y = 3 cosine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option C
D
y = negative 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2
Option D
10

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation , where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. Which equation also models this situation?

Question illustration
A
t = negative 35 sine (StartFraction pi Over 6 EndFraction m) + 55
Option A
B
t = negative 35 sine (StartFraction pi Over 6 EndFraction (m + 3)) + 55
Option B
C
t = 35 sine (StartFraction pi Over 6 EndFraction m) + 55
Option C
D
t = 35 sine (StartFraction pi Over 6 EndFraction (m + 3)) + 55
Option D
11

What is the value of x in the diagram below?

Question illustration
A
StartFraction 18 Over StartRoot 3 EndRoot EndFraction
Option A
B
StartFraction 18 StartRoot 2 EndRoot Over StartRoot 3 EndRoot EndFraction
Option B
C
StartFraction 18 StartRoot 3 EndRoot Over StartRoot 2 EndRoot EndFraction
Option C
D
18 StartRoot 2 EndRoot
Option D
12

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation graphed below, where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. If the equation is , what are the values of a and k?

Question illustration
A
a = –60; k = 20
B
a = –50; k = 30
C
a = –30; k = 50
D
a = –20; k = 60
13

Which of the following is cot() sec() in simplified form?

Question illustration
A
csc
Option A
B
tan
Option B
C
–1
D
1
14

Which of the following is true for f(x) = –2sin(x) – 3?

A
The range of the function is the set of real numbers .
Option A
B
The graph of the function is the graph of f(x) = –2sin(x) shifted 3 units up.
C
The amplitude of the function is 2.
D
The period of the function is .
Option D
15

What are the exact values of the six trigonometric functions for radians?

Question illustration
A
sine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative one-half; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; secant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option A
B
sine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot
Option B
C
sine (Negative StartFraction 7 pi Over 6 EndFraction) = one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot
Option C
D
sine (Negative StartFraction 7 pi Over 6 EndFraction) = StartFraction StartRoot 3 EndRoot Over 3 EndFraction; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option D

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