If sin = 5/6 what is cos?

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