5. You are on the beach in Wasaga Beach, Ontario. At 2:00 PM on June 15th, the tide is high. At that time you find that the depth at the end of the pier is 1.5 meters. At 8:00 pm the same day, the tide is low, and you find that the depth of the water is 1.1 meters. Assuming the depth of the water varies sinusoidally with time:

a) Identify the key features of the sinusoidal function, and use them to sketch a graph showing two tide cycles.

b) Determine an equation to represent the tide in Wasaga Beach.

c) Determine the height of the water at 11:00 PM the same day.

d) Determine the first two times after high tide where the height of the water is 1.2 metres.