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Math Help - Find x in trig equation

  1. #1
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    Find x in trig equation

    Hi there,

    My problem reads

    "Solve 6sin2x + sinx - 2 for all x in 0 < x < pi/2"

    I know through graphing that the answer is pi/6. Is there another way of proving this?

    thanks
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  2. #2
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    Re: Find x in trig equation

    You may also treat it as a quadratic equation and then the values can be found. For ax^2 + bx + c = 0; we have x = [ -1 +/- sqrt ( b^2- 4ac )]/ 2a
    In this case you will get sin x = [ -1 +/- sqrt ( 1+ 48 )]/ 12
    now solve it further
    Thanks from Caddym89
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  3. #3
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    Re: Find x in trig equation

    So I get sin x = 1/2 and -2/3.

    How do I then solve x for x in 0 < x < pi/2? Is it simply 1/2?
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  4. #4
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    Re: Find x in trig equation

    Sin pi/6 = 1/2 and sine is positive in first and second quadrant. Thus we have sin pi/ 6 = sin ( 5pi/6 ) = 1/2
    i hope it is ok now similarly for the other value. remember sine is negative in third and fourth quadrant.
    Thanks from Caddym89
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