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Math Help - help for a trigonometric problem

  1. #1
    Newbie
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    Apr 2009
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    help for a trigonometric problem

    Can anyone please give me some idea for this problem?
    The instantaneous power, p, in an electric circuit is given by p = iv,
    where v is the voltage and i is the current.
    Calculate the maximum value of power in the circuit if v=0.02 sin(100 pi t)volts and i=0.6 sin(100pi t+ pi/4 ) amp
    Calculate the first time that the power reaches a maximum value.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
    Posts
    1,458
    Hi

    p = iv=0.02 \sin(100 \pi t) \:0.6 \sin\left(100 \pi t+ \frac{\pi}{4}\right)

    Using
    \cos(a-b)-\cos(a+b))" alt="\sin a \:\sin b = \frac12\\cos(a-b)-\cos(a+b))" />

    Spoiler:

    p = 0.006 \:\left(\cos\left(\frac{\pi}{4}\right) - \cos\left(200 \pi t+ \frac{\pi}{4}\right)\right)

    p = 0.003 \:\sqrt{2} - 0.006\:\cos\left(200 \pi t+ \frac{\pi}{4}\right)

    The maximum is obtained when cos = -1

    p_{max} = 0.003 \:\sqrt{2} + 0.006 = 0.010\: W

    It is obtained for 200 \pi t+ \frac{\pi}{4} = \pi \implies t = \frac{3}{800} = 0.00375\:s
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