# Modeling with sinusoidal functions

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### Problem

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