Question 1011248
Easier way to view is right triangle of one leg 3 for x, other leg 6 for y and hypotenuse  {{{sqrt(9+36)=sqrt(45)=3sqrt(5)}}}.


sine is {{{sin(x)=6/(3sqrt(5))=2/sqrt(5)}}}, and because of where you find your terminal side, this will be {{{sin(x)=-2/sqrt(5)}}}.  You could rationalize the denominator if you want.  Finally, you want {{{highlight(csc(x)=-sqrt(5)/2)}}}.