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Math Help - Solve: e^x = 4 sin x

  1. #1
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    Solve: e^x = 4 sin x

    Solve the equation, e^x=4sinx ; x is greater than 0, less than 2pi.
    how do i figure this out, and i have my ti-83 with me.
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  2. #2
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    equation

    Hello,

    If you use your TI-83, you could simply punch in the function:

    f(x)=e^{x}

    g(x)=4\sin(x)

    The x you are searching for is the x-value at the intersection between the graphs of f and g.
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  3. #3
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    Quote Originally Posted by mathnerd501 View Post
    Solve the equation, e^x=4sinx ; x is greater than 0, less than 2pi.
    how do i figure this out, and i have my ti-83 with me.
    graph y = e^x - 4\sin{x} and calculate the zero(s) in the given interval.
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  4. #4
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    Can you input 'Ans' in your calculator (portable)? That means it can memorize the value obtained before and use the value in other calculation.

    Set it to be about  0.5

    Then input

     \ln( 4\sin(Ans) ) and press ' Enter' followed by ' Enter' ,' Enter',' Enter',' Enter',.... until no observable change on the screen , then the value displayed on it is the solution . It is  1.364958434...

    The key to find out the solution is to put one of the variable x as the subject . Here we can put  x = \ln(4\sin(x)) or  x = \sin^{-1}(\frac{e^x}{4})

    I also obtain the other solution ,  0.370558096...
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