The beam from an island lighthouse completes one rotation ev

The beam from an island lighthouse completes one rotation every two minutes. At time t (in minutes), the distance d (in miles) between the closest point on shore to the island and the light on the shoreline is given by d(t) = 3 tan (pi t). Find d(0.15), d(0.25) and d(0.45). What happens to the distance d as t approaches 1/2?

Solution

d(t) = 3 tan (pi*t )

a) d (.15) plug t = .15 = 3 tan ( pi*.15) = 1.5285 miles

d (.25) = 3 tan ( pi*.25) = 3 miles

d (.45) = 3 tan (pi*.45) = 18.941 miles