cos = √11 / 6
sin and cos have the same denominator, which is 6 because:
sin = opp/hyp
cos = adj/hyp
then to solve for cos with given sin use the trigonometric identity:
sin^2 + cos^2 = 1
(5/6)^2 + cos^2 = 1
cos^2= 1 - (5/6)^2
cos = √(1 - (5/6)^2)
cos = √(1 - 25/36)
cos = √(36/36 - 25/36)
cos = √(11/36)
cos = √11/√36
cos = √11/6