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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

Verified Answer :

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

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