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Math Help - Sinusoidal Functions

  1. #1
    Junior Member
    Joined
    Dec 2008
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    35

    Smile Sinusoidal Functions

    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.

    Joanie
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  2. #2
    Senior Member
    Joined
    Dec 2007
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    Melbourne
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    My answer: y=9.67sin(t/6.17pi - 2.68pi/6.17) + 12.25
    The phase shift term should be positive: the standard form is y = Asin(b(x-c))+k
    Also, the question is asking for a cosine function.
    Apart from that, looks good.

    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
    Excellent

    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.
    You need to add 5 for the "relative to lowest point bit" as that part tells you that the lowest point is considered 0 and hence the average will be 5. The negative sign out the front shouldn't be there.
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  3. #3
    Junior Member
    Joined
    Dec 2008
    Posts
    35

    Reply to Your Post

    12/14/o8

    Thank you for responding so promptly. You have been a real help.

    Joanie
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