Use the identity: #tan(theta) = y/x#:
#tan(theta) = 2/-sqrt(5)#
Rationalize the denominator:
#tan(theta) = (-2sqrt(5))/5#
Use the identity: #cot(theta) = 1/tan(theta)#
#cot(theta) = -sqrt(5)/2#
Use the identity #tan^2(theta) + 1 = sec^2(theta)#
#4/5 + 1 = sec^2(theta)#
#sec^2(theta) = 9/5#
#sec(theta) = +-3/sqrt(5)#
Rationalize the denominator:
#sec(theta) = +- (3sqrt(5))/5#
Please observe that the point #(-sqrt(5),2)# is in the second quadrant and the secant is negative in the second quadrant, therefore, we drop the + sign:
#sec(theta) = (-3sqrt(5))/5#
Use the identity #cos(theta) = 1/sec(theta)#:
#cos(theta) = -sqrt(5)/3#
Use the identity #tan(theta) = sin(theta)/cos(theta)#:
#sin(theta) = tan(theta)cos(theta)#
#sin(theta) = (2/-sqrt(5))( -sqrt(5)/3)#
#sin(theta) = 2/3#
Use the identity: #csc(theta) = 1/sin(theta)#:
#csc(theta) = 3/2#
