QUICK! 75 POINTS !!Select all that are part of the solution set of csc(x) > 1 and over 0 ≤ x ≤ 2π.

Answer:[tex]\frac{\pi}{4}[/tex] [tex]\frac{5\pi}{6}[/tex]Step-by-step explanation:The answer uses the unit circle and that sine and cosecant are reciprocals. The first choice doesn't even fit the criteria that [tex]x[/tex] is between [tex]0[/tex] and [tex]2\pi[/tex] (inclusive of both endpoints) because of the [tex]x=\frac{-7\pi}{6}[/tex].Let's check the second choice.[tex]\csc(\frac{\pi}{4})=\frac{2}{\sqrt{2}} \text{ since } \sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}[/tex].[tex]\csc(\frac{\pi}{4})>1 \text{ since } \frac{2}{\sqrt{2}}>1[/tex][tex]\csc(\frac{\pi}{2})=1 \text{ since } \sin(\frac{\pi}{2})=1[/tex] which means [tex]\csc(\frac{\pi}{2})=1[/tex] which is not greater than 1.So we can eliminate second choice.Let's look at the third.[tex]\csc(\frac{5\pi}{6})=2 \text{ since } \sin(\frac{5\pi}{6})=\frac{1}{2}[/tex] which means [tex]\csc(\frac{5\pi}{6})>1[/tex].[tex]\csc(\pi)[/tex]  isn't defined because [tex]\sin(\pi)=0[/tex].So we are eliminating 3rd choice now.Let's look at the fourth choice.[tex]\csc(\frac{7\pi}{6})=-2 \text{ since } \sin(\frac{7\pi}{6})=\frac{-1}{2}[/tex] which means [tex]\csc(\frac{7\pi}{6})<1[/tex] and not greater than 1.I was looking at the rows as if they were choices.Let me break up my choices.So we said [tex]x=-\frac{7\pi}{6}[/tex] doesn't work because it is not included in the inequality [tex]0\le x \le 2\pi[/tex].How about [tex]x=0[/tex]?  This leads to [tex]\csc(0)[/tex] which doesn't exist because [tex]\sin(0)=0[/tex].So neither of the first two choices on the first row.Let's look at the second row again.We said [tex]\frac{\pi}{4}[/tex] worked but not [tex]\frac{\pi}{2}[/tex]Let's look at the choices on the third row.We said [tex]\frac{5\pi}{6}[/tex] worked but not [tex]x=\pi[/tex]Let's look at at the last choice.We said it gave something less than 1 so this choice doesn't work.