On a particular Tuesday in a coastal​ town, the high tide occurs at 8​:12 AM. At that​ time, the water at the end of the pier is 11 ft deep. At 2​:24 ​PM, it is low tide and the water is only 7 ft deep. Assume the depth of the water is a sinusoidal function of time with a period of​ 1/2 a lunar​ day, which is about 12 hr 24 min. Answer the following questions. What was the approximate depth of the water at 4​:00 AM and at 9​:00 ​PM?