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Thread: is this answer wrong?trig

  1. #1
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    is this answer wrong?trig

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

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

    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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    $\displaystyle 8\cos^2{\theta} + 2\sin{\theta} = 7$

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

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

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

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

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

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

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

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

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

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