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Thread: Finding Largest Magnitude

  1. #1
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    Finding Largest Magnitude

    Suppose that at any given time t (in second) the current i (in amperes) in an alternation current circuit is i=2cost+2sint
    What is the peak current for this circuit. ( The largest magnitude)

    Thanks in advance
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  2. #2
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    Re: Finding Largest Magnitude

    Have you tried finding the maximum point of i by differentiating it? Alternatively, you can convert sin(t) + cos(t) to just sine using these formulas.
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  3. #3
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    Re: Finding Largest Magnitude

    I'm sorry that did not help me at all
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  4. #4
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    Re: Finding Largest Magnitude

    This is a calculus subforum. One of the best-known facts in calculus is Fermat's theorem.

    Also, I assume you know how to find the maximum of $\displaystyle A\sin(t+\varphi)$ for some constants A and $\displaystyle \varphi$. The link in post #2 shows a formula for converting 2sin(t) + 2cos(t) into $\displaystyle Asin(t+\varphi)$ for some A and $\displaystyle \varphi$.

    If this is not clear, please explain precisely what your difficulty is and what methods you know for finding maxima of functions.
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  5. #5
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    Re: Finding Largest Magnitude

    So you have a problem like this and have never taken Calculus? That makes it a little harder but it can be done.

    You know, I hope, that sin(a+ b)= cos(a)sin(b)+sin(a)cos(b). Taking b= x, you could use that immediately if you could have cos(a)= sin(a)= 2 but that is impossible because that would mean $\displaystyle cos^2(a)+ sin^2(a)= 4+ 4= 8$ which, of course, can't be true because $\displaystyle cos^2(a)+ sin^2(a)= 1$ for all a.

    But we can fix that: rewrite 2sin(x)+ 2cos(x) as $\displaystyle 2\sqrt{2}(1/(\sqrt{2})cos(x)+ 1/(\sqrt{3})sin(x))$. Now, we can say that $\displaystyle cos(a)= sin(a)= 1/(\sqrt{2})$ because then $\displaystyle sin^2(a)+ cos^2(a)= 1/2+ 1/2= 1$ as required.

    So we can write
    $\displaystyle 2sin(x)+ 2cos(x)= 2\sqrt{2}(1/\sqrt{2}cos(x)+ 1/\sqrt{2}sin(x))$
    $\displaystyle = 2\sqrt{2}(sin(\pi/4)cos(x)+ cos(\pi/4)sin(x))= 2\sqrt{2}sin(x+ \pi/4)$.

    Now use the fact that cos(x) has a maximum value of 1.
    Last edited by HallsofIvy; Apr 24th 2012 at 02:50 PM.
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  6. #6
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    Re: Finding Largest Magnitude

    Quote Originally Posted by HallsofIvy View Post
    you could use that immediately if you could have cos(a)= sin(a)= 2 but that is impossible
    My ROTC officer used to say that in wartime, the value of sine can reach 2, and by the order of the commander-in-chief, even 4
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