Based on the identity `sin^2(theta) + cos^2(theta) = 1`, we can solve for `cos(theta)` as follows:
`(sin(theta))^2 + (cos(theta))^2 = 1`
Substituting `sin(theta) = 5/6`:
`(5/6)^2 + (cos(theta))^2 = 1`
Simplifying:
`25/36 + (cos(theta))^2 = 1`
`(cos(theta))^2 = 1 - 25/36`
`(cos(theta))^2 = 11/36`
Taking the square root of both sides:
`cos(theta) = +/- sqrt(11)/6`
Since we know that `sin(theta) = 5/6`, we can conclude that `cos(theta)` is the positive value `cos(theta) = sqrt(11)/6`.
Therefore, `cos(theta) = sqrt(11)/6`.