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Math Help - [SOLVED] Trig Help required

  1. #1
    stuckbigtime
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    [SOLVED] Trig Help required

    Question is v=240sin(100 pi t-pi/6) i=30cos(100 pi t+pi/3)
    power = V x i
    find max power and time it first occurs

    I have expanded v to give me (207.84sin 100 pi t-120 cos 100 pi t)
    and expanded i to give me (15 cos 100 pi t - 25.98 sin 100 pi t)

    multiply v x i gives me
    3117.6 sin 100 pi t cos 100 pi t - 5399.68sinē 100 pi t - 1800 cosē 100 pi t + 3117.6 cos 100 pi t sin 100 pi t

    not too sure if I have my + and - in correct places after I have multiplied and i'm stuck after that about how to get my max power and time answers ??
    any help would be greatful its quite a big question
    Last edited by stuckbigtime; March 5th 2008 at 01:56 AM.
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by stuckbigtime View Post
    Question is v=240sin(100 pi t-pi/6) i=30cos(100 pi t+pi/3)
    power = V x i
    find max power and time it first occurs

    I have expanded v to give me (207.84sin 100 pi t-120 cos 100 pi t)
    and expanded i to give me (15 cos 100 pi t - 25.98 sin 100 pi t)

    multiply v x i gives me
    3117.6 sin 100 pi t cos 100 pi t - 5399.68sinē 100 pi t - 1800 cosē 100 pi t + 3117.6 cos 100 pi t sin 100 pi t

    not too sure if I have my + and - in correct places after I have multiplied and i'm stuck after that about how to get my max power and time answers ??
    any help would be greatful its quite a big question
    P = 240 \sin \left( 100 \pi t - \frac{\pi}{6} \right) \times 30 \cos \left( 100 \pi t + \frac{\pi}{3} \right)

     = 7200 \sin \left( 100 \pi t - \frac{\pi}{6} \right) \cos \left( 100 \pi t + \frac{\pi}{3} \right).

    Now use the product rule to get dP/dt. Then solve dP/dt = 0 for t. Test the nature - keep the maximum. Substitute this value of t into P to get maximum P.
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