The equation d is equal to 11 cosine open paren 8 pi over 5 t close paren models the horizontal distance, d , in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t , in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance.
A complete trip from the rightmost position to the leftmost position and back is one full cycle of the cosine model. For d = 11 cos((8π/5)t), the angular frequency is 8π/5, so the period is 2π ÷ (8π/5) = 10/8 = 1.25 seconds. Therefore, the pendulum takes 1.25 seconds, choice D.
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