Exercise 82 Page 971

Practice makes perfect

a We are asked to find the period and amplitude of the graph of

f (x)

f (x) = 2 cos (4 x)

We can do this without graphing it. To do so, let's recall the general form of a cosine function.

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b Now we will graph

f (x)

over two periods. Let's first sketch only one cycle. To do so we will use the information that we found in Part A.

Amplitude : 2 Period : \frac{π}{2}

Now, to plan our sketch of the graph we will divide the period into fourths to plot the five-point pattern.

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c This time we will find the value which gives

0.5 .

To do so, we will set

f (x)

0.5

and then solve it for

x .

0.5 = 2 cos (4 x) \Rightarrow 0.25 = cos (4 x)

Now, we will use the inverse cosine function to isolate

4 x .

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Exercises p.964-971