If sin x = .42, what is cos x?

You can make use of the relationship
  sin^2 + because^2 = 1
to solve for because. You get
  because^2 = 1 - sin^2
  because = Sqrt[1 - sin^2]
For your value of sin, this is
  because = Sqrt[1 - .42^2]
  because = Sqrt[1 - .1764]
  because = Sqrt[.8236]
  because ~~ .9075

The value of because(x) is approximately .9075