Answer:
A
Step-by-step explanation:
Cos(theta) = -2/5
From sin^2(theta) + cos^2(theta) = 1 we get
sin^2(theta) = 1 - cos^2(theta)
sin(theta) = sqrt(1 - cos^2(theta)). The root is the positive one in quad 2
sin(theta) = sqrt(1 - cos^2(theta))
sin(theta) = sqrt(1 - (-2/5)^2)
sin(theta) = sqrt(1 - 4/25)
sin(theta) = sqrt(21/25)
sin(theta) = sqrt(21)/5
csc(theta) = 1/sin(theta)
csc(theta) = 1/sqrt(21)/5
csc(theta) = 5/sqrt(21)
The answer should be the denominator rationalized as in
csc(theta) = 5 * sqrt(21) / 21.
However that is not an option, so the answer is A
