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AP Precalculus · Question of the Day

AP Precalculus Question of the Day

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Friday, August 7, 2026

Using the equation y=sin⁡(12x)y=\sin\left(\tfrac{1}{2}x\right) for a pendulum, what is the period?

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Question of the Day

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Using the equation y=sin⁡(12x)y=\sin\left(\tfrac{1}{2}x\right) for a pendulum, what is the period?

  1. The period is π\pi.
  2. The period is 4π4\pi. (correct answer)
  3. The period is 2π2\pi.
  4. The period is 1/21/2.

Explanation: This question tests AP Precalculus skills: understanding sine and cosine function transformations, specifically period changes with fractional coefficients. The period formula is period = 2π/|B| for y = sin(Bx), where smaller B values create larger periods (slower oscillations). For y = sin(1/2·x), B = 1/2, so period = 2π/(1/2) = 2π × 2 = 4π, meaning the pendulum takes twice as long to complete one cycle. Choice B correctly identifies the period as 4π, showing the function oscillates half as fast as standard sine. Choice A incorrectly suggests π; Choice C suggests the standard 2π; Choice D confuses period with the coefficient. To help students: when B is a fraction, remember that dividing by a fraction means multiplying by its reciprocal. Visualize that smaller B values stretch the graph horizontally.