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Math Help - is this answer wrong?trig

  1. #1
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    is this answer wrong?trig

    Q find in radians, all the values of \theta between -\pi and \pi satisfying the equation

    8cos^2\theta+2sin\theta=7

    the answers are 0.524 2.261 which i get but i dont get 3.386 or 6.034 instead i get -14.5 degrees and hence 180-14.5 can any see where I have gone wrong or is it the answers thnx.!
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  2. #2
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    8\cos^2{\theta} + 2\sin{\theta} = 7

    8(1 - \sin^2{\theta}) + 2\sin{\theta} = 7

    8 - 8\sin^2{\theta} + 2\sin{\theta} = 7

    0 = 8\sin^2{\theta} - 2\sin{\theta} - 1

    0 = (4\sin{\theta} + 1)(2\sin{\theta} - 1)

    \sin{\theta} = -\frac{1}{4}

    {\theta} = \arcsin\left(-\frac{1}{4}\right)

    {\theta} = -\left[\pi + \arcsin\left(-\frac{1}{4}\right)\right]

    \sin{\theta} = \frac{1}{2}

    \theta = \frac{\pi}{6}

    \theta = \frac{5\pi}{6}
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