Question 672645
Use the given information to find exact values of cos(x/2), sin(x/2), and tan(x/2):
tan x = 2, pi < x < 3pi/2
**
Given information shows that x is in quadrant III, where cos<0, sin<0, tan>0
tanx=2=opp side/adj side=2/1
hypotenuse=&#8730;(2^2+1^2)=&#8730;(4+1)=&#8730;5
sinx=opp side/hypotenuse=-2/&#8730;5
cosx=adj side/hypotenuse=-1/&#8730;5
..
use half-angle identities to solve
cos(x/2)=±[&#8730;(1+(cosx)/2)]
=-[&#8730;(1-(1/&#8730;5)/2)]
=-[&#8730;(&#8730;5-1)/2&#8730;5)]
..
sin(x/2)=±[&#8730;(1-(cosx)/2)]
=-[&#8730;(1+(1/&#8730;5)/2)]
=-[&#8730;(&#8730;5+1)/2&#8730;5)]
..
tan(x/2)=sinx/(1+cosx)
=-2&#8730;5/(1-(1/&#8730;5)
=-2&#8730;5/(&#8730;5-1)/&#8730;5
=-2/&#8730;5-1