If cos(x)=1/4 what is sin(x) and tan(x)

You can use the identity
  cos(x)² +sin(x)² = 1
to find sin(x) from cos(x) or vice versa.

  (1/4)² +sin(x)² = 1
  sin(x)² = 1 - 1/16
  sin(x) = ±(√15)/4

Then the tangent can be computed as the ratio of sine to cosine.
  tan(x) = sin(x)/cos(x) = (±(√15)/4)/(1/4)
  tan(x) = ±√15

There are two possible answers.
In the first quadrant:
  sin(x) = (√15)/4
  tan(x) = √15

In the fourth quadrant:
  sin(x) = -(√15)/4
  tan(x) = -√15