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10-30.

When delivering a crane to the port of Oakland, the company delivering the crane had to wait for low tide in order to clear the Bay Bridge. At low tide, the maximum clearance for the bridge is $186$ feet. At high tide the maximum clearance is $178$ feet. The crane required a clearance of $184$ feet. If low tide occurred at 9:20 a.m. and high tide was at 2:50 p.m., find the earliest and latest time for the crane to be able to clear the bridge.

Write a sinusoidal function to represent this situation.

Graph some points from the situation to help you determine its equation. Assume $t = 0$ is 12:00 a.m.

Set your equation equal to $178$ and solve for $t$.

$y=4\cos\left(\frac{\pi}{5.5}(x-9.333)\right)+182$