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math/calculus

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an electric current I , in amps is given by:
I= cos(wt) + sqrt of 3 sin(wt)
where w is positive constant. what are the max and minimum values of I?
*please be specific

  • math/calculus -

    dI/dt = -wsin wt + w√3cos wt
    = 0 for max min

    wsin wt = w√3cos wt
    sin wt/cos wt = w√3/w = √3
    tan wt = pi/3 or 4pi/3

    if wt = pi/3
    I = cos pi/3 + √3sin pi/3 = .5 + 1.5 = 2
    if wt = 4pi/3
    I = cos 4pi/3 + √3sin 4pi/3 = -.5 -1.5 = -2

  • math/calculus -

    so it could be pi/3 or 4pi/3
    which means both are correct?
    should i put both answers or one answer on my final paper?

  • math/calculus -

    The pi/3 yields the maximum, notice I = +2
    and the 4pi/3 yields the minimum

    The actual question was, "what are the max and min values of I"
    max of I is 2
    min of I is -2

    the pi/3 and 4pi/3 produce those max and mins, they themselves are not the max and mins.

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