## Algebra and Trigonometry 10th Edition

x = $\frac{\pi}{6}$, $\frac{5\pi}{6}$, $\frac{3\pi}{2}$
Note: csc(x) = $\frac{1}{sin(x)}$ $csc^{2}(x) - csc(x) - 2 = 0$ The expression can be factored as follows: (csc(x) - 2) (csc(x) + 1) = 0 Since the expression is equal to 0, it can be split as follows: csc(x) - 2 = 0 and csc(x) + 1 = 0 csc(x) - 2 = 0 can be manipulated and solved as follows: csc(x) = 2 $\frac{1}{sin(x)} = 2$ sin(x) = $\frac{1}{2}$ x = $\frac{\pi}{6}$, $\frac{5\pi}{6}$ csc(x) + 1 = 0 can be manipulated and solved as follows: csc(x) = -1 $\frac{1}{sin(x)} = -1$ sin(x) = -1 x = $\frac{3\pi}{2}$ The solutions are: x = $\frac{\pi}{6}$, $\frac{5\pi}{6}$, $\frac{3\pi}{2}$