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Math Help - Trigonometric equation

  1. #1
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    Trigonometric equation

    Can anybody help me with this equation? I am staring to think there is a mistake there....
    I tried to factor it, but it does not seem right...

    2sin^2(x) - 6sin(x)- 3=0
    Last edited by Angie80; July 17th 2010 at 04:35 PM.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Hint:

    Quadratic equation.
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  3. #3
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    Hint 2:

    |sin(x)| \leq 1
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  4. #4
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    This is what I tried:
    sinx=t
    2t^2-6t-3=o
    I used quadratic formula, and got:
    t= ( 3- √15) /2 = -0.43

    What now? I could substitute t for sinx now, but it does not help...
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  5. #5
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    Quote Originally Posted by Angie80 View Post
    This is what I tried:
    sinx=t
    2t^2-6t-3=o
    I used quadratic formula, and got:
    t= ( 3- √15) /2 = -0.43

    What now? I could substitute t for sinx now, but it does not help...
    Exact solutions:

    Let x_1 = \frac{3 - \sqrt{15}}{2}. Then \sin (x) = x_1 \Rightarrow x = \sin^{-1} (x_1) + 2 n \pi or x = \sin^{-1} (-x_1) + \pi + 2 n \pi (using the symmetry of the unit circle) where n is an integer.

    Approximate solutions:

    Use a calculator to get a decimal approximation of \sin^{-1} \left( \frac{3 - \sqrt{15}}{2} \right) and then proceed in the usual way.
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  6. #6
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    So, I calculated it and got appx: -26
    I must be missing something, because I really do not know how to proceed from here...
    I know how to use unit circle, but what is value of x, when sinx=-26??

    I am veeery confused now....
    Last edited by Angie80; July 17th 2010 at 04:48 PM.
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  7. #7
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    Quote Originally Posted by Angie80 View Post
    So, I calculated it and got appx: -26
    I must be missing something, because I really do not know how to proceed from here...
    I know how to use unit circle, but what is value of x, when sinx=-26?? Mr F says: No. x = -26, not sinx.

    I am veeery confused now....
    sin is negative in the 3rd and 4th quadrants. Using degrees, in the 4th quadrant, x = -26 + (360)n. In the 3rd quadrant, x = (180 + 26) + (360)n by symmetry of the unit circle.

    Go back and review examples from your class notes and textbook.
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  8. #8
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    Thanks soooo much!
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