Given that tan theta 611 and sin theta Solutiontan theta611

Given that tan theta = -6/11 and sin theta

tan theta=-6/11

opposite=6 and adjacent=11

hypotenuse=sqrt(36+121)=sqrt 157

cot theta=1/tan theta=-11/6

csc theta=hypotenuse/opposite=-sqrt157/6

sin(2pi + theta)=sin theta=opposite/hypotenuse=-6/sqrt 157

csc(- theta) = -csc theta=-(-sqrt157)/6=sqrt157/6