You can put this solution on YOUR website! What is the value of csc (-19pi/3)?
(-19π/3)=(-18π/3-π/3)=(-6π-π/3)=3(2π) revolutions +π/3 clockwise.
you are working with a reference angle, π/3 in quadrant IV where csc and sin<0
csc (-19pi/3)=-csc(π/3)=1/-sin(π/3)=1/-(√3/2)=-2/√3=-2√3/3