# In a certain costal area, the depth of water may be approximated by a sinusoidal function of the form d(t) = – 2.5 cos[ b(t – 2) ] + 3.5,

Because of the gravitational attractions of the moon and the sun on the Earth, water in seas and oceans tend to rise and fall periodically corresponding to what is called high and low tides. In a a typical situation, the time between two high tides is close to 12 hours. In a certain costal area, the depth of water may be approximated by a sinusoidal function of the form d(t) = – 2.5 cos[ b(t – 2) ] + 3.5, where d is in meters and t in in hours where t = 0 corresponds to 12 am.

a) Find b (b > 0) if d has a period of 12 hours.

b) From t =0 to t = 12, at what time is d the smallest (low tide) and at what time it is highest (high tide)?

c) From t = 0 to t = 12, what are the interval of time during which the depth of the water 4.5 meters or more?