If csc theta=-5/4 and theta is between 180 and 270 what is the value of cos

To solve the question for cos θ will be found as follows:

csc θ=-5/4

but

csc θ=1/sin θ

thus

sin θ=-4/5

thus

θ=arcsin (-4/5)

θ=-53.130

but since the value lies between 180 and 270, our value will be:

180 - (-53.130) = 233.16

thus

cos233.16=-0.59958