Answer:
first option: Harulo is correct because the angle is coterminal with 3π / 4 and the reference angle is π / 4.
Step-by-step explanation:
1) 19 π/4 = 4π + 3 π/4, which is 4 complete turns and 3/4 of turn.
2) 3 π/4 is in the third quadrant, so the reference angle is π - 3 π/4 = π/4
3) sin (π/4) = sin (3π/4) = (√2) / 2
4) csc (π/4) = 1 / [ sin (3π/4) ] = 1 / [ (√2) / 2 ] = 2 / (√2) = √2, which shows the validity of the statement and csc(19π/4) = √2.