Graphing Sine and Cosine Functions

Question 1

Which graph represents the function

Revolt · Accepted Answer

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).

Question 2

What is the y-intercept of the function ?

Revolt · Accepted Answer

(0, negative one-half)

Question 3

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

Revolt · Accepted Answer

Decrease a.

Question 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?

Revolt · Accepted Answer

Let a > 1 or a < –1.

Question 5

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

Revolt · Accepted Answer

The amplitude increases, and the period increases.

Question 6

What is one characteristic of the cosine function?

Revolt · Accepted Answer

Its graph is symmetric about the y-axis.

Question 7

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

Revolt · Accepted Answer

0, π, and 2π

Question 8

Which statement illustrates why cosine is an even function?

Revolt · Accepted Answer

Cosine (negative StartFraction pi Over 4 EndFraction) = cosine (StartFraction 4 pi Over 4 EndFraction)

Question 9

Which function has a period of 4π?

Revolt · Accepted Answer

y = one-half sine (one-half x)

Question 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?

Revolt · Accepted Answer

Decrease b.

Graphing Sine and Cosine Functions Answers

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