document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866238>Question 866238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the given expression.\r<BR>\n" );
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document.write( "tan(1/2 cos^-1(2/3)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522159 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=522159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the given expression. <BR>\n" );
document.write( "tan(1/2 cos^-1(2/3))<BR>\n" );
document.write( "let x=angle whose cos=2/3<BR>\n" );
document.write( "cosx=2/3<BR>\n" );
document.write( "sinx=&#8730;(1-cos^2x)=&#8730;(1-4/9)=&#8730;(5/9)=&#8730;5/3<BR>\n" );
document.write( "tan(1/2 cos^-1(2/3))=tan(x/2)<BR>\n" );
document.write( "Identity: tan(x/2)=sinx/(1+cosx)=(&#8730;5/3)/(1+(2/3))=(&#8730;5/3)/(5/3)=&#8730;5/5<BR>\n" );
document.write( "calculator check:<BR>\n" );
document.write( "cosx=2/3<BR>\n" );
document.write( "x&#8776;48.19&#730;<BR>\n" );
document.write( "x/2&#8776;24.09<BR>\n" );
document.write( "tan(x/2)&#8776;tan(24.09)&#8776;0.4471…<BR>\n" );
document.write( "exact value as calculated=&#8730;5/5&#8776;0.4471… </SPAN>\n" );
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