Modeling with sinusoidal functions

Vlad is playing on a swing set.

His horizontal distance $D(t)$D, left parenthesis, t, right parenthesis (in $\text{m}$start text, m, end text) from the center (where being behind the center means a negative distance) as a function of time $t$t (in seconds) can be modeled by a sinusoidal expression of the form $a\cdot\cos(b\cdot t)+d$a, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d.

At $t=0$t, equals, 0, when he pushes off, he is $1\text{ m}$1, start text, space, m, end text behind the center, which is as far back as he goes. The swing reaches the center $\dfrac{\pi}{6}$start fraction, pi, divided by, 6, end fraction seconds later.

$D(t) =$D, left parenthesis, t, right parenthesis, equals