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## Q. 5.3.3

Graphing another periodic function

Sketch the graph of y = -3 cos x for x in the interval [-2π, 2π] and find its amplitude.

## Verified Solution

Make a table of ordered pairs for x in [0, 2π] to get one cycle of the graph. Note that the five x-coordinates in the table divide the interval [0, 2π] into four equal parts. Multiply the y-coordinates of y = cos x by -3 to obtain the y-coordinates for y = -3 cos x.

$\begin{array}{r|c|c|c|c|c} x & 0 & \pi / 2 & \pi & 3 \pi / 2 & 2 \pi \\ \hline y=-3 \cos x & -3 & 0 & 3 & 0 & -3 \end{array}$

Draw one cycle of y = -3 cos x through these five points, as shown in Fig. 5.45. Repeat the same shape for x in the interval [-2π, 0] to get the graph of y = -3 cos x for x in [-2π, 2π]. The amplitude is $|0.5(3-(-3))|$ or 3.