Given sin θ =3/5 and 0 < θ < π/ 2, find the exact value of the function sin θ/2.

Answer 1

sinx = 3/5 = opposite side/hypotenuse

cosx = 4/5 = adjacent side/hypotenuse

5^2 = 4^2 + 3^2

25 = 16 + 9

sin(x/2) = + or - sqr(1-cosx)/2 = + sqr(1-4/5)/2 = - sqr(1/5/2) = sqr(1/10), ignore the negative root as x is in the 1st quadrant, and so is x/2.

sin(x/2) = 1/sqr10 = sqr10/10 = about 3.16/10 = 0.316

Answer 2

sin θ = 3/5 → cos θ = 4/5

sin θ/2 = √((1 - cos θ) / 2)

Answer 3

Please see video.