Question

What is the solution to the trigonometric inequality 2-3csc(x) > 8 over the interval radians?

Answer 1

`2 - 3csc(x) > 8 \\ 2 - (3)/(sin(x)) > 8 \\ - 6 > (3)/(sin(x)) \\ - 2 > (1)/(sin(x)) \\ ( - 1)/(2) < sin(x) \: \: or \: \: \: sin(x) > ( - 1)/(2) \\ \\`

`sin( ( - \pi)/(6) ) = ( - 1)/(2)`

`x \: in \: \: [0, (7\pi)/(6)[U] (11 \pi )/(6) ,2\pi] + 2k\pi`

Answer 2

D. pi<x<7pi/6 and 11pi/6<x<2

Explanation:

Took the test and this is the correct answer