Chapter 6: Q 17. (page 409)

Determine the amplitude and period of each function without graphing.
$y = - \frac{1}{2} \cos (\frac{3}{2} x)$ .

Short Answer

Expert verified

Amplitude is $\frac{1}{2}$ and period is $\frac{4 π}{3}$ .

Step by step solution

Step 1. Given Information.

Determine the amplitude and period of each function without graphing.

$y = - \frac{1}{2} \cos (\frac{3}{2} x)$ .

Step 2. Evaluation.

For $ω > 0$ , the amplitude and period of $y = A \cos (ω x)$ are given by

amplitude $= |A|$ , Period $= T = \frac{2 π}{ω}$ .

After comparing the equation, we get

$A = |- \frac{1}{2}| = \frac{1}{2}$ , $ω = \frac{3}{2}$

Then, $T = \frac{2 π}{\frac{3}{2}} = \frac{4 π}{3} .$

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Determine the amplitude and period of each function without graphing.
$y = - \frac{1}{2} \cos (\frac{3}{2} x)$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Evaluation.

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One App. One Place for Learning.

Most popular questions from this chapter

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Determine the amplitude and period of each function without graphing.
$y = - \frac{1}{2} \cos (\frac{3}{2} x)$ .