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Math Help - circular functions

  1. #1
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    circular functions

    the temperature T C inside a house at a time t hours after 6.00 am is given by T=18-4cos(pi t/12) for 0\leqslant t\leqslant 24

    the temperature \theta C outside a house at time t hours after midnight is given by \theta =11-6cos(pi t/12) for 0\leqslant t\leqslant 24

    if the difference between the inside and outside temperatures can be represented by D=T-\theta , sketch the graph of D. determine when the difference between inside and the outside temperature is less then 6C.

    guys anyideas?
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  2. #2
    MHF Contributor

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    Yes- that you should show some effort yourself first! All you are asked to do is subtract two functions. One thing to be carfule about- the variable "t" in the two equations represent two different things. In the formula for "T", t is "hours after 6.00 am" while in the formula for " \theta", t is "hours after midnight".

    If we call the "t" in the formula for T t' so we can distinguish then t'= t- 6 because, of course, 6 am is 6 hours after midnight.
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  3. #3
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    so for function T & theta, you substitute 6 into the equation. which will give you 18 and 11. 6pm and 11am
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