Determine solution of the equation in radians Find sin x2 gi

Determine solution of the equation in radians. Find sin x/2, given that sin x=1/4 and x terminates in O<x<pi/2. *Use the Half-Angle Identity.

Solution

sinx = 1/4 ; x terminates in 0<x<pi/2

cosx = sqrt( 1- sin^2x) = sqrt( 1- 1/16) = sqrt(15)/4

Half Angle Formula : sin(x/2) = sqrt[ (1+cosx)/2]

= sqrt[ (1+ sqrt(15)/4)/2]

= sqrt[( 4+sqrt(15))/8]