# Modeling with sinusoidal functions

Given the description of a real-world relationship, find the sinusoidal function that models it.
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### Problem

Vlad is playing on a swing set.
His horizontal distance D, left parenthesis, t, right parenthesis (in m) from the center (where being behind the center means a negative distance) as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d.
At t, equals, 0, when he pushes off, he is 1, space, m behind the center, which is as far back as he goes. The swing reaches the center start fraction, pi, divided by, 6, end fraction seconds later.
Find D, left parenthesis, t, right parenthesis.