Question

Find the exact value of csc 5pi/6

Answer 1

csc 2 (csc
`(5\pi)/(6)` = csc 150 = csc 30 = csc 2)

Explanation:

csc
`(5\pi)/(6)` is in the 2nd Quadrant where only sin, and csc are positive.

csc
`((5\pi)/(6))=csc (\pi -((5\pi)/(6)))=csc((5\pi)/(6))`

but csc
`(5\pi)/(6)` =
`(1)/(sin (\pi/6)) = (1)/(sin 30) = (1)/(1/2) =2`