Find each of the following 17 sin x 45 and 3 pi2 Solutiongi

Find each of the following 17 sin x = -4/5 and 3 pi/2

Solution

given : sinx = -4/5 where 3pi/2 <x<2pi

cosx = 3/5 (cos is +ve in IVrth quadrant)

sin(x/2)

use the formula: sin(x/2) = sqrt(( 1-cosx)/2)

= sqrt(( 1-3/5)/2)

= sqrt( 1/5)

= 1/sqrt5