SOLUTION: Find exact Value of tan Beta/2, Given that tanBeta = square root 5/2 and pi < Beta < 3pi/2 So I think Beta/2 is in quadrant 3 making it positive but I tried square root of 5 as t

Question 959220: Find exact Value of tan Beta/2, Given that tanBeta = square root 5/2 and pi < Beta < 3pi/2
So I think Beta/2 is in quadrant 3 making it positive but I tried square root of 5 as the answer and thats wrong please help!!!!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find exact Value of tan Beta/2, Given that tanBeta = square root 5/2 and pi < Beta < 3pi/2
***
use x for Beta
tanx=√5/2 (In quadrant III)
hypotenuse of reference right triangle in quadrant III=√(√5)^2+2^2)=√(5+4)=3
sinx=√5/3
cosx=2/3
tan(x/2)=sinx/(1+cosx)
tan(x/2)=√5/3/(1+2/3)=√5/3/5/3=√5/5
Check:
tanx=√5/2
x=48.1897˚
x/2≈24.0948˚
tan(x/2)≈tan(24.0948)≈0.4472
exact value=√5/5≈0.4472
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