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