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


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.
should be in radians.
D, left parenthesis, t, right parenthesis, equals