### Home > PC3 > Chapter 12 > Lesson 12.2.1 > Problem12-106

12-106.

A barge delivering a crane to the port of Oakland has to wait for lower tides 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 requires a clearance of $184$ feet. Tomorrow, low tide occurs at 9:20 a.m. and high tide occurs at 2:50 p.m. For what time intervals will the crane be able to clear the bridge?

Write a sinusoidal function to represent this situation. Let $y = \text{the clearance (not the tide height)}$.

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

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