AnswersPrecalculusGraphing Sine and Cosine Functions

Graphing Sine and Cosine Functions — Quiz Answers

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1
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Which statement illustrates why cosine is an even function?

A
cosine of open paren pi over 4 close paren is equal to negative cosine times open paren 4 pi over 4 close paren
B
cosine of open paren negative pi over 4 close paren is equal to cosine of open paren pi over 4 close paren
C
cosine of open paren pi over 4 close paren is equal to negative cosine times open paren 5 pi over 4 close paren
D
cosine of open paren the fraction with numerator negative 7 pi and denominator 6 close paren is equal to cosine of open paren 5 pi over 4 close paren
2
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Which graph represents the function y is equal to 2 sine open paren 1 half x close paren ?

A
Image with description 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).
B
Image with description 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).
C
Image with description 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.
D
Image with description 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).
3

Which graph represents the function y is equal to negative 2 cosine open paren 2 pi x close paren ?

A
Image with description 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).
B
Image with description 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).
C
Image with description 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).
D
Image with description 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).
4

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

A
y is equal to 2 sine open paren 4 pi x close paren
B
y is equal to 2 sine open paren 1 half x close paren
C
y is equal to 1 half sine open paren 4 pi x close paren
D
y is equal to 1 half sine 2 x
5

If the function y is equal to sine x is transformed to y is equal to 3 sine open paren 2 thirds x close paren , how do the amplitude and period change?

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

On the interval 0 is less than or equal to x comma x is less than or equal to 2 pi , what are the x -intercepts of y is equal to sine x ?

A
0 , pi , and 2 pi
B
mathrm pi over 2 and 3 pi over 2 only
C
0 , pi over 2 , and 3 pi over 2
D
pi and 2 pi only
7

What is one characteristic of the cosine function?

A
Its graph is symmetric about the y -axis.
B
Its domain is between negative 1 and 1 and is inclusive.
C
It is an odd function.
D
It has a period equal to pi .
8

Consider the function y is equal to A cosine b x , where A is greater than 0 and b is greater than 0 Which change affects the locations of the x -intercepts of the graph?

A
Decrease b .
B
Change the sign of b .
C
Change the sign of A .
D
Decrease A .
9

Which function has a period of 4 pi ?

A
y is equal to 4 sine x
B
y is equal to 1 half sine open paren 1 half x close paren
C
y is equal to 2 sine 2 x
D
y is equal to sine of open paren 1 fourth x close paren
10

Consider the function y is equal to A sine b x , where A is greater than 0 and b is greater than 0 Which change compresses the graph vertically?

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

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