find sin(x/2) if tanx=4/3 and pi<x<(3pi/2)

Question

this is a math problem im stuck on...

Answer 1

It's a 3-4-5 right triangle

if tanx = 4/3, in the quadrant III, then sinx = -4/5 and cosx =-3/5

sin(x/2) = + or - sqr((1-cosx)/2)

= + or - sqr(1+3/5)/2) = + or - sqr(4/5) = + or - 2sqr.2 = about .894

check the answer

tanx = 4/3

x = tan^-1(4/3) = about 53.13 or for quadrant III x=180+53.13 = 233.13

x/2 = 233.13 = 116.56

sin(x/2) = sin116.56 = 0.894

x/2 is in quadrant II where sines are all positive