Answers IC Pre-Cal - DeeringAngles and Trigonometric Functions

Graphing Sine and Cosine Functions Answers

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

Increase a.

Decrease a.

Increase b.

Decrease b.

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

0, StartFraction pi Over 2 EndFraction, and StartFraction 3 pi Over 2 EndFraction

0, π, and 2π

StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 2 EndFraction

π and 2π only

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?

Let a < 0.

Let a > 0.

Let a > 0 and a < 1.

Let a > 1 or a < –1.

What is one characteristic of the cosine function?

It is an odd function.

It has a period equal to π.

Its graph is symmetric about the y-axis.

Its domain is between –1 and 1 and is inclusive.

Which statement illustrates why cosine is an even function?

Cosine (StartFraction pi Over 4 EndFraction) = negative cosine (StartFraction 5 pi Over 4 EndFraction)

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

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

Cosine (StartFraction negative 7 pi Over 6 EndFraction) = cosine (StartFraction 5 pi Over 4 EndFraction)

Review the table.

Negative one-half, negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, negative one-half

One-half, StartFraction StartRoot 2 EndRoot Over 2 EndFraction, StartFraction StartRoot 3 EndRoot Over 2 EndFraction

StartFraction StartRoot 3 EndRoot Over 2 EndFraction, StartFraction StartRoot 2 EndRoot Over 2 EndFraction, one-half

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?

y = three-halves sine (26 pi x)

y = three-halves sine (524 pi x)

y = 3sin(262πx)

y = 3sin(524πx)

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

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).

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).

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).

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).