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Math Help - Circular Functions Application

  1. #1
    Junior Member
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    Circular Functions Application

    Question Is:

    It is suggested that the height h(t) meters of the tide above mean sea level on 1st january at Warnung is given approximately by the rule h(t) = 4sin(pi/6t), where t is the number of hours after midnight.

    A) when was high tide?
    B) what was the height of the tide?
    C) what was the height of the tide at 8 am?
    D) a boat can only cross the harbour bar when the tide is atleast 1 meter above mean sea level. when could the boat cross the harbour bar on 1st january?

    please i need help with this
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  2. #2
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    Oct 2010
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    If I understand the question (as I'm not so good in English):
    answers
    A) the sinus function is maximum at pi/2, 2pi+pi/2, 4pi+pi/2, ..., 2n*pi + pi/2...
    pi/6 * t = pi/2 , you get t = 3
    pi/6 * t = 2pi +pi/2 = 5pi/2 , you get t = 15
    pi/6 * t = 4pi +pi/2 = 9pi/2 , you get t = 27 (which is greater then the number of the hours in one day)
    So high tide was at 3 and 15 (3pm).
    B) the maximum value of the sinus function is 1, so 4*1 = 4
    C) just put t = 8: 4sin(pi/6 * 8) = 4sin(pi * 4/3) = 4 * (-0.5) = -2
    D) You must find when h is 1. 1 = 4sin(pi/6t), with the calculator (put the DRG to radians!!!) you can find sin-1 of 1/4 is 0.25268... so t = 0.48...
    If you sketch the tide you can see that it goes down under 1 again at 6-0.48=5.52 (because of symmetry). And the situation repeats after 12 hours. So the boat can cross from 0.48 to 5.52 and from 12.58 to 17.52.
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