Question 959220
Find exact Value of tan Beta/2, Given that tanBeta = square root 5/2 and pi < Beta < 3pi/2 
***
use x for Beta
tanx=&#8730;5/2 (In quadrant III)
hypotenuse of reference right triangle in quadrant III=&#8730;(&#8730;5)^2+2^2)=&#8730;(5+4)=3
sinx=&#8730;5/3
cosx=2/3
tan(x/2)=sinx/(1+cosx)
tan(x/2)=&#8730;5/3/(1+2/3)=&#8730;5/3/5/3=&#8730;5/5
Check:
tanx=&#8730;5/2
x=48.1897&#730;
x/2&#8776;24.0948&#730;
tan(x/2)&#8776;tan(24.0948)&#8776;0.4472
exact value=&#8730;5/5&#8776;0.4472