If cosine of x equals 1 over 2, what is sin(x) and tan(x)?

If cos x = 1/2, to find x  we can use formula , 

sin² x + cos² x=1
sin²x = 1- cos ² x
sin²x=1-(1/2)² =3/4

sin²x =3/4
√(sin²x)=+/-√(3/4)=√(3)/2

sin x= √(3)/2, and sin x= - √(3)/2,

tan x = sin x/cos x
tan x = √(3)/2/(1/2)= √(3), and tan x = -√(3)/2/(1/2)= -√(3)

sin x= √(3)/2, and sin x= - √(3)/2,
tan x = √(3), and tan x = -√(3)

If you need only positive values you can use, sin x= √(3)/2, 
tan x = √(3).

The answer is option c.