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Q. 5.3.6

Changing the period

Graph two cycles of y = sin(2x) and determine the period of the function.

Verified Solution

The graph of y = sin x completes its fundamental cycle for 0 ≤ x ≤ 2π. So y = sin(2x) completes one cycle for 0 ≤ 2x ≤ 2π, or 0 ≤ x ≤ π. Thus the period is π. For 0 ≤ x ≤ p, the x-intercepts are (0, 0), (π/2, 0), and (π, 0). Midway between 0 and π/2, at x = π/4, the function reaches a maximum value of 1, and the function attains its minimum value of -1 at x = 3π/4. Draw one cycle of the graph through the x-intercepts and through (π/4, 1) and (3π/4, -1). Then graph another cycle of y = sin(2x) as shown in Fig. 5.50.