Given that sin x = 1/2 calculate cos x .

To calculate the value of the function cosine, we'll apply
the fundamental formula of trigonometry:

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

cos x = sqrt [1-(sin
x)^2]

cos x = sqrt (1 - 1/4), but sin x =
1/2

cos x = sqrt[(4-1)/4]

cos
x = (sqrt3)/2 , if x is in the first quadrant, namely x belongs to the interval (0,
pi/2).

cos x = -(sqrt3)/2, if x is in the second quadrant,
namely x belongs to the interval (pi/2, pi).