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Math Help - Help with trigonomic equation...

  1. #1
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    Help with trigonomic equation...

    i am supposed to find all solutions in [0,2pi). the original equation is

    4sin^2x - 3sinx - 2 = 0

    i started off using the quadratic formula and got

    3 +/- sqrt|-3^2 - 4*4*-2 / 2*4
    after simplifying all these through i was left with 3 +/- sqrt41/8

    this is where i am confused and really have no idea where to continue, there really isn't a problem to explain this in the book so any help would be great.
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  2. #2
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    Re: Help with trigonomic equation...

    Put these in your calculator

    \displaystyle  \sin^{-1}\left( \frac{3+ \sqrt{41}}{8}\right)

    and

    \displaystyle  \sin^{-1}\left( \frac{3- \sqrt{41}}{8}\right)

    What do you get?
    Last edited by pickslides; July 18th 2011 at 04:22 PM.
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  3. #3
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    Re: Help with trigonomic equation...

    do you mind explaining how to do that?
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  4. #4
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    Re: Help with trigonomic equation...

    I accidently edited post #2
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  5. #5
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    Re: Help with trigonomic equation...

    when i do i get domain error

    when i do the other one i get -25.1754 rounded
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  6. #6
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    Re: Help with trigonomic equation...

    Quote Originally Posted by lolcheelol View Post
    when i do i get domain error

    when i do the other one i get -25.1754 rounded
    do you understand how the inverse trig functions work and how to interpret what the calculator is telling you?

    Pauls Online Notes : Calculus I - Review : Trig Equations with Calculators, Part I
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  7. #7
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    Re: Help with trigonomic equation...

    Quote Originally Posted by skeeter View Post
    do you understand how the inverse trig functions work and how to interpret what the calculator is telling you?

    Pauls Online Notes : Calculus I - Review : Trig Equations with Calculators, Part I
    yes i do, but usually i get stuff like like sin^-1(sqrt3/2) and ill end up with pi/3. so im not exactly sure how this answer is supposed to be written out. i can't find anything like it in my notes and in the book :/
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  8. #8
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    Re: Help with trigonomic equation...

    Quote Originally Posted by lolcheelol View Post
    yes i do, but usually i get stuff like like sin^-1(sqrt3/2) and ill end up with pi/3. so im not exactly sure how this answer is supposed to be written out. i can't find anything like it in my notes and in the book :/
    you're used to solving equations whose solutions are unit circle values ... this equation requires the use of a calculator, hence the reason for the link. have a look.
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  9. #9
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    Re: Help with trigonomic equation...

    awesome, thanks a lot for the help. i had done a little bit of that in my notes, but nothing that explained. GREATLY appreciated!
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