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Math Help - Sin Graph - x coordinates help

  1. #1
    Junior Member 22upon7's Avatar
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    Sin Graph - x coordinates help

    Hi,

    I'm working on my application task exercises for Trigonometric graphs, but I can't seem to work this sum out, A step by step explanation would be great:

    The depth,
    D(t) metres, of water at the entrance to a harbour at t hours after midnight on a particular day is given by D(t) = 10 + 3 sin (\frac{\pi t}{6}), 0 \leq t \leq 24

    1. Find the value of t for which D(t) \geq 8.5


    Any help would be greatly appreciated,

    Thanks,

    Dru
    Last edited by 22upon7; September 2nd 2009 at 02:52 AM.
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by 22upon7 View Post
    Hi,

    I'm working on my application task exercises for Trigonometric graphs, but I can't seem to work this sum out, A step by step explanation would be great:

    The depth, D(t) metres, of water at the entrance to a harbour at t hours after midnight on a particular day is given by D(t) = 10 + 3 sin (\frac{\pi t}{6}), 0 \leq t \leq 24

    1. Find the value of t for which D(t) \geq 8.5

    Any help would be greatly appreciated,

    Thanks,

    Dru
    Draw the graph of D = 10 + 3 \sin \left(\frac{\pi t}{6}\right), 0 \leq t \leq 24. Draw the graph of D = 8.5. The intervals for which D \geq 8.5 should be clear. And it should also be clear why you should now solve 8.5 = 10 + 3 \sin \left(\frac{\pi t}{6}\right), 0 \leq t \leq 24 ....
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