What is sin 2x if cos x=1/2, 0

We notice that the values of the angle x are located in
the 1st and the 2nd quadrants.

We'll apply the double angle
identity:

sin 2x=sin(x+x)=sin x*cos x + cos x*sin x = 2sin
x*cos x

Since the value of cos x is positive the given
interval (0,pi) is stretching to (0,pi/2), because the cosine function is positive only
in the first quadrant, in the second quadrant being
negative.

The value for sin x is also positive in the 1st
quadrant and it could be found using Pythagorean
identity.

(sin x)^2 = 1-(cos
x)^2

(sin x)^2 = 1 - 1/4

sin x
= (sqrt 3)/2

sin 2x = 2sin x*cos
x

sin 2x=
2(sqrt3/2)(1/2)

The requested value of sin 2x
is: sin 2x= (sqrt3)/2.