AnswersPre Calculus AGraphing Sine and Cosine Functions

Graphing Sine and Cosine Functions Answers

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1
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Which graph represents the function

Question illustration
A
On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at 8 pi. The curve crosses the y-axis at negative 2.
Option A
B
On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at 4 pi. The curve decreases through y-axis at (0, 0).
Option B
C
On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at 8 pi. The curve crosses the y-axis at (0, 2).
Option C
D
On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at 4 pi. The curve increases through the y-axis at (0, 0).
Option D
2
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What is the y-intercept of the function ?

Question illustration
A
(negative one-half, 0)
Option A
B
(0, negative one-half)
Option B
C
(0, three-halves)
Option C
D
(Three-halves, 0)
Option D
3

Consider the function y = asin(bx), where a > 0 and b > 0. Which change compresses the graph vertically?

A
Increase a.
B
Decrease a.
C
Increase b.
D
Decrease b.
4

The musical note E can be modeled by the function, y = asin(1320πx), where a = 1 and x is the time in seconds. Playing note E on your computer, you notice that it is not loud enough to be heard across the room.What change can you make to the function to make note E louder than the original?

A
Let a < 0.
B
Let a > 0.
C
Let a > 0 and a < 1.
D
Let a > 1 or a < –1.
5

If the function y = sinx is transformed to , how do the amplitude and period change?

Question illustration
A
The amplitude increases, and the period decreases.
B
The amplitude increases, and the period increases.
C
The amplitude decreases, and the period decreases.
D
The amplitude decreases, and the period increases.
6

What is one characteristic of the cosine function?

A
It is an odd function.
B
It has a period equal to π.
C
Its graph is symmetric about the y-axis.
D
Its domain is between –1 and 1 and is inclusive.
7

On the interval 0 ≤ x ≤ 2π, what are the x-intercepts of y = sinx?

A
0, StartFraction pi Over 2 EndFraction, and StartFraction 3 pi Over 2 EndFraction
Option A
B
0, π, and 2π
C
StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 2 EndFraction
Option C
D
π and 2π only
8

Which statement illustrates why cosine is an even function?

A
Cosine (StartFraction pi Over 4 EndFraction) = negative cosine (StartFraction 5 pi Over 4 EndFraction)
Option A
B
Cosine (StartFraction pi Over 4 EndFraction) = negative cosine (StartFraction 4 pi Over 4 EndFraction)
Option B
C
Cosine (negative StartFraction pi Over 4 EndFraction) = cosine (StartFraction 4 pi Over 4 EndFraction)
Option C
D
Cosine (StartFraction negative 7 pi Over 6 EndFraction) = cosine (StartFraction 5 pi Over 4 EndFraction)
Option D
9

Which function has a period of 4π?

A
y = one-half sine (one-half x)
Option A
B
y = sine (one-fourth x)
Option B
C
y = 2sin(2x)
D
y = 4sin(x)
10

Consider the function y = acos(bx), where a > 0 and b > 0. Which change affects the locations of the x-intercepts of the graph?

A
Decrease a.
B
Decrease b.
C
Change the sign of a.
D
Change the sign of b.
11

Which graph represents the function y = –2cos(2πx)?

A
On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at StartFraction 2.5 pi Over 4 EndFraction. It crosses the y-axis at (0, negative 2).
Option A
B
On a coordinate plane, a function has a maximum of 2 and minimum of 2. It completes one period at one-fourth pi. It crosses the y-axis at (0, negative 2).
Option B
C
On a coordinate plane, a function has a maximum of 2 and minimum of 2. It completes one period between StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 4 EndFraction. It decreases through the y-axis at (0, 0).
Option C
D
On a coordinate plane, a function has a maximum of 2 and minimum of 2. It completes one period between StartFraction pi Over 4 EndFraction and StartFraction pi Over 2 EndFraction. It decreases through the y-axis at (0, 0).
Option D
12

What is the equation of a sine function with an amplitude of 2 and a period of 4π?

A
y = one-half sine (2 x)
Option A
B
y = one-half sine (4 pi x)
Option B
C
y = 2 sine (one-half x)
Option C
D
y = 2 sine (4 pi x)
Option D
13

The middle note C has a frequency of 262 hertz and can be modeled using a sine function with an amplitude of 1.5, where x is time in seconds.Which function represents the vibrations of this note?

A
y = three-halves sine (26 pi x)
Option A
B
y = three-halves sine (524 pi x)
Option B
C
y = 3sin(262πx)
D
y = 3sin(524πx)
14

Review the table.

Question illustration
A
Negative one-half, negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option A
B
Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, negative one-half
Option B
C
One-half, StartFraction StartRoot 2 EndRoot Over 2 EndFraction, StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option C
D
StartFraction StartRoot 3 EndRoot Over 2 EndFraction, StartFraction StartRoot 2 EndRoot Over 2 EndFraction, one-half
Option D

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