If cosine of x equals 1 over 2, what is sin (x) and tan (x) ? Explain your steps in complete sentences.

So far, I found that adjacent=1 and hypotenuse=2, but I have no idea where to go from there

Sin² x+cos²x=1 ⇒sin x=⁺₋√ (1-cos² x)

tan x=sin x / cos x

sin x=⁺₋√ (1 - (1/2) ²) = ⁺₋√ (1-1/4) = ⁺₋√ (3/4) = ⁺₋√3 / 2

so, sin x can be:

sin x=-√3 / 2

sin x=√3 / 2

if sin x=-√3/2, then: tan x = (-√3/2) / 1/2=-√3.

if sin x=√3/2; then tan x = (√3/2) / (1/2) = √3.

Answer: if cos x=1/2; the sin of x can be equal to - √3 / 2 or √3 / 2; and tan x can be equal to - √3 or √3. it depends of the quadrant:

First quadrant: cos x=1/2; sin x=√3 / 2; tan x=√3

fourth quadrant: cos x=1/2; sin x=-√3 / 2; tan x=-√3