Find the exact values of the remaining trigonometric functio

Find the exact values of the remaining trigonometric functions of theta, from the information given. sec theta = -6/5, sin theta

sec theta=-6/5 , sin theta <0

Here both sec theta and sin theta are negative. It means theta is in third quadrant, where tan and cot are positive .

cos theta =1/sec theta =-5/6

sin theta=sqrt(1-cos²theta) =-sqrt(1-(25/36)) =-sqrt(11)/6

csc theta=1/sin theta = -6/sqrt(11)=-6 sqrt(11)/11

tan theta=sin theta/cos theta =sqrt(11)/5

cot theta =1/tan theta=5/sqrt(11)=5sqrt(11)/11