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- Thread starter melissax
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To find the range of the given sinusoid, I would use this method:

$\displaystyle -1\le\cos(x)\le1$

$\displaystyle -A\le A\cos(x)\le A$

$\displaystyle B-A\le A\cos(x)+B\le B+A$

Can you apply this procedure to the function you are given?

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You have found the correct range, but what you actually want to do is this:

Begin with the fact that the cosine function varies from -1 to 1:

$\displaystyle -1\le\cos(x)\le1$

Multiply through by the given amplitude of 5:

$\displaystyle -5\le 5\cos(x)\le5$

Add through by the given vertical displacement of 3:

$\displaystyle 3-5\le 5\cos(x)+3\le3+5$

Simplify:

$\displaystyle -2\le 5\cos(x)+3\le8$

And this demonstrates the range is [-2,8].

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