document.write( "Question 959220: Find exact Value of tan Beta/2, Given that tanBeta = square root 5/2 and pi < Beta < 3pi/2
\n" ); document.write( "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!!!! \n" ); document.write( "
Algebra.Com's Answer #586353 by lwsshak3(11628)\"\" \"About 
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Find exact Value of tan Beta/2, Given that tanBeta = square root 5/2 and pi < Beta < 3pi/2
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\n" ); document.write( "use x for Beta
\n" ); document.write( "tanx=√5/2 (In quadrant III)
\n" ); document.write( "hypotenuse of reference right triangle in quadrant III=√(√5)^2+2^2)=√(5+4)=3
\n" ); document.write( "sinx=√5/3
\n" ); document.write( "cosx=2/3
\n" ); document.write( "tan(x/2)=sinx/(1+cosx)
\n" ); document.write( "tan(x/2)=√5/3/(1+2/3)=√5/3/5/3=√5/5
\n" ); document.write( "Check:
\n" ); document.write( "tanx=√5/2
\n" ); document.write( "x=48.1897˚
\n" ); document.write( "x/2≈24.0948˚
\n" ); document.write( "tan(x/2)≈tan(24.0948)≈0.4472
\n" ); document.write( "exact value=√5/5≈0.4472 \n" ); document.write( "
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