Find the exact value of sin and csc. Rationalize all denominators

Question

The given point (2, -1) is on the terminal side of an angle in standard position. Find the exact value of sin and csc. Rationalize all denominators

Answer 1

Calculate hypotenuse.

x = 2 and y = -1

hypotenuse, r=√(2^2+(-1)^2) =√5

sin theta =y/r =-1/√5

csc theta =r/y =√5/-1=-√5