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Precalculus : Graphing the Sine and Cosine Functions

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Example Questions

Example Question #51 : Graphing The Sine And Cosine Functions

What is the amplitude of F(t)=5sin(2x-1) ?

Possible Answers:

Correct answer:

Explanation:

The formula for the amplitude of a sine function is from the form:

F(t)=Asin(Bt-C)+D .

In our function, A=5 .

Therefore, the amplitude for this function is .

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Example Question #52 : Graphing The Sine And Cosine Functions

Find the amplitude of the following trig function: $y=-2-3sin(2\theta-5)$

Possible Answers:

$\frac{3}{2}$

Correct answer:

Explanation:

Rewrite $y=-2-3sin(2\theta-5)$ so that it is in the form of:

y=Asin(Bx+C)+D

$y=-3sin(2\theta-5)-2$

The absolute value of is the value of the amplitude.

$\textup{Amplitude= }\left | A\right |= \left | -3\right |=3$

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Example Question #4 : Find The Amplitude Of A Sine Or Cosine Function

Find the amplitude of the function.

$y=5sin\, x$

Possible Answers:

Correct answer:

Explanation:

For the sine function

$y=Asin\, x$ where $A\epsilon \, \mathbb{R}$

the amplitude is given as $\left | A\right |$ .

As such the amplitude for the given function

$y=5sin\, x$ is

$\left | 5\right |=5$ .

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Example Question #3 : Period And Amplitude

Which of the given functions has the greatest amplitude?

Possible Answers:

$2\sin(x)$

$\sin\frac{2\pi }{3}(x+2)$

$\frac{1}{2}\sin(4x)$

$\sin(x+3)$

$\sin(4x)$

Correct answer:

$2\sin(x)$

Explanation:

The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is $2\sin(x)$ .

The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.

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Precalculus : Graphing the Sine and Cosine Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #51 : Graphing The Sine And Cosine Functions

Example Question #52 : Graphing The Sine And Cosine Functions

Example Question #4 : Find The Amplitude Of A Sine Or Cosine Function

Example Question #3 : Period And Amplitude

All Precalculus Resources

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