Question

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

Answer 1

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