Trig help- validate answer

http://prntscr.com/bmtnk

find csc(t)

well I got 5* sqrt(24)/24

but non of the answer matches, please help

Technically your answer is correct. You did not put negative since csc is negative in III quadrant and you have not simplified your answer

cos t = -1/5 and t is in III quadrant

since cos is adjacent side / hypotenuse , adjacent side = 1 and hypotenuse = 5

opposite side = SQRT(5^2 - 1^2) = SQRT(25 - 1) = SQRT(24) = 2√6

csc t = hypotenuse / opposite side = - 5 / 2√6 = - (5/12)√6 ( csc is negative in III quadrant )

t is in Q III so csc(t) is negative.
opposite side = -sqrt(24)
csc(t) = -5sqrt(24)/24
csc(t) = -10sqrt(6)24=
-5sqrt(6)/12