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## Q. 5.3.7

A period that is not a multiple of π

Determine the period of $y=\cos \left(\frac{\pi}{2} x\right)$ and graph two cycles of the function.

## Verified Solution

For this function, B = π/2. To find the period, use P = 2π/B:

$P=\frac{2 \pi}{\pi / 2}=4$

So one cycle of $y=\cos \left(\frac{\pi}{2} x\right)$ is completed for 0 ≤ x ≤ 4. The cycle starts at (0, 1) and ends at (4, 1). A minimum point occurs halfway in between, at (2, -1). The x-intercepts are (1, 0) and (3, 0). Draw a curve through these five points to get one cycle of the graph. Continue this pattern from 4 to 8 to get a second cycle, as shown in Fig. 5.51.