Thread: Need some help with a trig equation

1. 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.

2. Re: Need some help with a trig equation

Originally Posted by DEADTERMINATOR
"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*}