A toy boat is bobbing on the water.
Its distance D(t)D(t)D, left parenthesis, t, right parenthesis (in \text{m}mstart text, m, end text) from the floor of the lake as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\sin(b\cdot t)+da⋅sin(b⋅t)+da, dot, sine, left parenthesis, b, dot, t, right parenthesis, plus, d.
At t=0t=0t, equals, 0, when the boat is exactly in the middle of its oscillation, it is 1\text{ m}1 m1, start text, space, m, end text above the water's floor. The boat reaches its maximum height of 1.2\text{ m}1.2 m1, point, 2, start text, space, m, end text after \dfrac{\pi}{4}
4
π
​
start fraction, pi, divided by, 4, end fraction seconds.
Find D(t)D(t)D, left parenthesis, t, right parenthesis.