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Math Help - Need some help with a trig equation

  1. #1
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    Need some help with a trig equation

    "Algebraically solve csc x = 2 sin x +1 where 0\circ\leq\Theta\leq360\circ

    I find myself stuck on this question. Not sure why, it doesn't seem much more complex than what I've been doing. Some help as to what to do would be appreciated.
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  2. #2
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    Re: Need some help with a trig equation

    Quote Originally Posted by DEADTERMINATOR View Post
    "Algebraically solve csc x = 2 sin x +1 where 0\circ\leq\Theta\leq360\circ

    I find myself stuck on this question. Not sure why, it doesn't seem much more complex than what I've been doing. Some help as to what to do would be appreciated.
    \displaystyle \begin{align*} \csc{x} &= 2\sin{x} + 1 \\ \frac{1}{\sin{x}} &= 2\sin{x} + 1 \\ 1 &= 2\sin^2{x} + \sin{x} \\ 0 &= 2\sin^2{x} + \sin{x} - 1 \\ 0 &= 2\sin^2{x} + 2\sin{x} - \sin{x} - 1 \\ 0 &= 2\sin{x}(\sin{x} + 1) - 1(\sin{x} + 1) \\ 0 &= (\sin{x} + 1)(2\sin{x} - 1) \\ \sin{x} + 1 &= 0 \textrm{ or } 2\sin{x} - 1 = 0 \\ \sin{x} &= -1 \textrm{ or } \sin{x} = \frac{1}{2} \\ x &= 270^{\circ} \textrm{ or } x = \left\{ 30^{\circ}, 150^{\circ} \right\} \\ x &= \left\{ 30^{\circ}, 150^{\circ}, 270^{\circ} \right\}\end{align*}
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