find the exact value: sin[arccos(3^(1/2) / 4]

We'll use the formula
that:

sin(arccos x) = sqrt(1 - x^2)
(1)

We'll put x =
sqrt3/4

We'll raise to square both
sides:

x^2 = 3/16

We'll
substitute x in the expression (1):

sin(arccos sqrt3/4) =
sqrt(1 - 3/16)

sin(arccos sqrt3/4) =
sqrt[(16-3)/16]

sin(arccos sqrt3/4) =
(sqrt13)/4

sin(arccos sqrt3/4)
= 0.9013