At a location off a pier on the Maine coastline, the function d(t) = 4.36 cos(0.4991) + 8.79 models the depth d in feet of the water t hours after the first high tide during a first
quarter moon
a. Identify the amplitude and period of the function as well as the equation of the
midline. Describe the graph of this function as a series of transformations of the
parent function y = cosx.
b. Explain how you can use the cosine function from part A to write a sine function
to model the depth of the water. Describe the graph of this function as a series of
transformations of the parent function y = sinx.
c. The heights of astronomical tides are affected by the moon phase. A function that
models the depth of the water at the same location after the first low tide during a
new moon is d(t) = 6,31sin(0.503(t – 3.13)] + 8.75. Identify the amplitude and
period of the function as well as the equation of the midline. Describe the graph
of this function as a series of transformations of the parent function y = sinx.
d. Explain how you can use the sine function from part C on the previous page to
write a cosine function to model the height of the water. Describe the graph of
this function as a series of transformations of the parent function y = cos x.
e. Compare the functions from parts A and B with the functions from parts
C and D. How do the tides during a new moon compare to the tides during a
first quarter moon?