What is the period of y = A sin(Bx + C) in terms of B?

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Multiple Choice

What is the period of y = A sin(Bx + C) in terms of B?

Explanation:
Think of the period as the distance along the x-axis needed for the sine curve to complete one full cycle. For y = A sin(Bx + C), the inside angle Bx + C must advance by 2π to complete a cycle. As x increases by Δx, the inside angle increases by BΔx. Setting BΔx = 2π gives Δx = 2π/B. This Δx is the period. If B is negative, you still get a positive period by using 2π/|B|, so with the usual assumption B > 0, the period is 2π/B.

Think of the period as the distance along the x-axis needed for the sine curve to complete one full cycle. For y = A sin(Bx + C), the inside angle Bx + C must advance by 2π to complete a cycle. As x increases by Δx, the inside angle increases by BΔx. Setting BΔx = 2π gives Δx = 2π/B. This Δx is the period. If B is negative, you still get a positive period by using 2π/|B|, so with the usual assumption B > 0, the period is 2π/B.

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