document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=959220>Question 959220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find exact Value of tan Beta/2, Given that tanBeta = square root 5/2 and pi < Beta < 3pi/2 <BR>\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!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854572 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53875)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Find exact Value of tan(Beta/2), Given that tan(Beta) = square root 5/2 and pi < Beta < 3pi/2<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculations in the post by @lwsshak3 are fatally and totally incorrect.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is enough to notice that Beta is in QIII (given), hence, Beta/2 is in QII,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;so tan(Beta) must be negative, while @lwsshak3 gives a positive number as the answer.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;His checking procedure also is wrong.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Below is my correct solution.\r<BR>\n" );
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document.write( "use x for Beta<BR>\n" );
document.write( "tan(x) = √5/2 (given, so BETA is in QIII)<BR>\n" );
document.write( "hypotenuse of reference right triangle in quadrant III = √(√5)^2+2^2)=√(5+4)=3<BR>\n" );
document.write( "sin(x) = -√5/3 in QIII (negative)<BR>\n" );
document.write( "cos(x) = -2/3 in QIII (negative)<BR>\n" );
document.write( "tan(x/2) = sin(x)/(1+cos(x))<BR>\n" );
document.write( "tan(x/2) = (-√5/3)/(1-2/3) = (-√5/3)/(1/3) = -√5/1 = -√5.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "tan(x) = √5/2 in QIII<BR>\n" );
document.write( "x = 48.19° + 180° = 228.19°<BR>\n" );
document.write( "x/2 ≈ 114.095°<BR>\n" );
document.write( "tan(x/2) ≈ tan(114.095°) ≈ -2.236<BR>\n" );
document.write( "exact value = -√5 ≈ -2.236\r<BR>\n" );
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document.write( "Solved correctly and checked in a right way, too.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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