I have three problems--I want to verifyif I have the correct answers.
1. Eastport, Maine, has among the highest tides in the U.S.. Write a cosine function that models the oscillation of Eastport's tides if their amplitude is 9 feet 8 inches, the equilibrium is 12 feet 3 inches, the phase shift is -2.68 hours, and the period is 12.34 hours.
My answer: y=9.67sin(t/6.17pi - 2.68pi/6.17) + 12.25
2. The mean average temperature for Fairbanks, Alaska is 27 degrees F. The monthly average temperatures vary between 36.5 degrees above and below this value. If t=0 represents February, the phase shift of the sine function is 2.
a. Write a model for the average monthly temperature in Fairbanks.
My answer: y=36.5sin(t/6pi-pi/3)+27
b. According to your model what is the average temperature in November?
My answer: y(9) = 8.8 degrees
3. Stan observes a raft floating on the water bobbing up and down through a total amplitude of 5 feet. Beginning at the top of the wave, if the raft completes a full cycle every 5 seconds, what is the height of the raft relative to its lowest point after 32 seconds?
My answer: -5cos[2pi/5(32)]=4.04 ft.
If you can verify my answers, I would appreciate it. Thanks.