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Math Help - Maximization

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    62

    Maximization

    This may not even count as a calculus question, simply because I've already done the calculus part. I just don't know how to do the algebra to solve it haha. So if this needs to be moved, I apologize.

    Anyway! Here is the problem and what I've done:

    Problem: An electric current, I, in amps, is given by I = cos(Ct) + sqrt(3)sin(Ct) where C /= 0 is a constant. Find the minimum and maximum values of I. For what values of t will these occur if 0 <= t <= 2pi.

    My work:
    I know how to find the max and min values. I took the derivative, set it to 0, and began solving for t.

    \frac{dI}{dt} = \sqrt{3}C cos(Ct) - Csin(Ct)

    0 = \sqrt{3} C cos(Ct) - Csin(Ct)

    Factored out a c and got:

    0 = \sqrt{3}cos(Ct) - sin(Ct)

    So...how do I solve for t from this point? Do I use the arccosine and arcsine? I'm not sure...I just can't seem to remember how to do it!

    Thanks for any help!
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  2. #2
    Newbie
    Joined
    Jul 2008
    Posts
    16
    Quote:
    "




    Factored out a c and got:


    "
    add sin to both sides

    Sin(Ct)=root3 Cos(Ct)

    now square both sides

    sin^2(Ct)=3Cos(Ct)

    pythagorean identity

    1-cos^2(Ct)=3Cos(Ct)

    get on one side

    cos^2(Ct)+3Cos(Ct)-1=0

    use quadratic formula to find cos(Ct)
    one of the answers is -3.3ish which isn't possible
    for cos and the other is .30277 which is possible for cos
    so use that one.

    arccos(.30277) = 1.26 radians

    t=1.26/C

    just plug that answer back in to make sure i didn't screw up. Im pretty high right now so who knows? When ever you're doing trig stuff and theres sines and cosines all over the place, it helps to get all sines or all cosines with the help of identities. Practice makes perfect so don't stop hammering those problems.
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