At high tide, the depth of water in a tidal river is 6.3 meters, while at low tide the depth is 2.5 meters. Suppose that on January 20, the last high tide of the day is at 5 pm, and the last low tide is at 11:15 pm. Let d(t) be the depth of the water in the river, measured in meters, t hours after noon on January 20. Assume that d(t) is a sinusoidal function.

A docked boat requires a depth of 5.3 meters to set sail and the captain wants to get an early start on January 21st. Between what two times in the morning of January 21st can the boat set sail?

Question

At high tide, the depth of water in a tidal river is 6.3 meters, while at low tide the depth is 2.5 meters. Suppose that on January 20, the last high tide of the day is at 5 pm, and the last low tide is at 11:15 pm. Let d(t) be the depth of the water in the river, measured in meters, t hours after noon on January 20. Assume that d(t) is a sinusoidal function.

A docked boat requires a depth of 5.3 meters to set sail and the captain wants to get an early start on January 21st. Between what two times in the morning of January 21st can the boat set sail?