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Math Help - Trig

  1. #1
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    Trig

    The depth of water at the entrance to a harbour t hours after low tide is D metres and can be modelled by the equation D= a+ b cos[c(t+d)] for the constants a,b,c and d

    at t = 0, it is low tide and the depth is 2 metres.
    At the next high tide, 6 hours later, the depth is 8 metres.

    Find Exact values of a,b,c and given that all constants are positive..

    any help with this i dont even have a start :S
    thanks
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  2. #2
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    Quote Originally Posted by Tarik678 View Post
    The depth of water at the entrance to a harbour t hours after low tide is D metres and can be modelled by the equation D= a+ b cos[c(t+d)] for the constants a,b,c and d

    at t = 0, it is low tide and the depth is 2 metres.
    At the next high tide, 6 hours later, the depth is 8 metres.

    Find Exact values of a,b,c and given that all constants are positive..

    any help with this i dont even have a start :S
    thanks
    The formula has 4 coefficients you need to find, a, b, c, d. To do that you need 4 "conditions" or 4 equations. You are given:
    1. When t= 0, the depth is 2: 2= a+ bcos(d)
    2. 6 hours later, when t= 6, the depth is 8: 8= a+ bcos(6c+ d).
    3. When t= 0, the depth is minimum. The minimum of cos(x) is -1 and occurs when x= -\pi/2: 2= a- b and d= -\pi/2.
    4. When5 t= 6, the depth is maximum. The maximum of cos(x) is 1 and occurs when x= \pi/2: 8= a+ b and 6c+ d= \pi/2.
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