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Precalculus : Find the Amplitude of a Sine or Cosine Function

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Example Question #1 : Find The Amplitude Of A Sine Or Cosine Function

What is the amplitude of $y=3\sin\left(\frac{x}{5}\right)}$ $\displaystyle y=3\sin\left(\frac{x}{5}\right)}$?

Possible Answers:

$\displaystyle 5$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\displaystyle 3$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\displaystyle 1$

Correct answer:

$\displaystyle 3$

Explanation:

For any equation in the form $y=a\sin(bx)$ $\displaystyle y=a\sin(bx)$, the amplitude of the function is equal to $\left | a\right |$ $\displaystyle \left | a\right |$.

In this case, a=3 $\displaystyle a=3$ and $b=\frac{1}{5}$ $\displaystyle b=\frac{1}{5}$, so our amplitude is $\displaystyle 3$.

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Example Question #51 : Graphing The Sine And Cosine Functions

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

Possible Answers:

$\displaystyle -1$

$\displaystyle 8$

$\displaystyle 5$

$\displaystyle 3$

Correct answer:

$\displaystyle 5$

Explanation:

The formula for the amplitude of a sine function is $\displaystyle A$ from the form:

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

In our function, A=5 $\displaystyle A=5$.

Therefore, the amplitude for this function is $\displaystyle 5$.

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Example Question #1 : Find The Amplitude Of A Sine Or Cosine Function

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

Possible Answers:

$\displaystyle 3$

$\displaystyle -2$

$\displaystyle 2$

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

$\displaystyle -3$

Correct answer:

$\displaystyle 3$

Explanation:

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

$\displaystyle y=Asin(Bx+C)+D$

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

The absolute value of $\displaystyle A$ is the value of the amplitude.

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

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

Find the amplitude of the function.

$y=5sin\, x$ $\displaystyle y=5sin\, x$

Possible Answers:

$\displaystyle 5$

$\displaystyle 1$

$\displaystyle 10$

$\displaystyle x$

Correct answer:

$\displaystyle 5$

Explanation:

For the sine function

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

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

As such the amplitude for the given function

$y=5sin\, x$ $\displaystyle y=5sin\, x$ is

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

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Example Question #1 : Trigonometric Graphs

Which of the given functions has the greatest amplitude?

Possible Answers:

$\sin(x+3)$ $\displaystyle \sin(x+3)$

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

$2\sin(x)$ $\displaystyle 2\sin(x)$

$\sin(4x)$ $\displaystyle \sin(4x)$

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

Correct answer:

$2\sin(x)$ $\displaystyle 2\sin(x)$

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 $2\sin(x)$ $\displaystyle 2\sin(x)$.

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 : Find the Amplitude of a Sine or Cosine Function

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Find The Amplitude Of A Sine Or Cosine Function

Example Question #51 : Graphing The Sine And Cosine Functions

Example Question #1 : Find The Amplitude Of A Sine Or Cosine Function

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

Example Question #1 : Trigonometric Graphs

All Precalculus Resources

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