document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=516629>Question 516629</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Use the information given about angle theta to find the exact value of cosine theta/2\r<BR>\n" );
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document.write( "sin theta=3/5 and 0<theta<pie/2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344425 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=344425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "First use the Pythagorean Identity to find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \cos\theta\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\varphi\ =\ 1\ -\ \sin^2\varphi\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\theta\ =\ 1\ -\ \frac{9}{25}\ =\ \frac{16}{25}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\theta\ =\ \pm\frac{4}{5}\">\r<BR>\n" );
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document.write( "But recall <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\ <\ \theta\ <\ \frac{\pi}{2}\">, hence <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \theta\"> is a 1st quadrant angle, therefore the cosine is positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\theta\ =\ \frac{4}{5}\">\r<BR>\n" );
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document.write( "Now use the half angle formula for cosine:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\frac{\theta}{2}\ =\ \pm\sqrt{\frac{1\ +\ \cos\theta}{2}}\">\r<BR>\n" );
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document.write( "But recall <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\ <\ \theta\ <\ \frac{\pi}{2}\">, hence <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\ <\ \frac{\theta}{2}\ <\ \frac{\pi}{4}\">, is also a 1st quadrant angle, therefore the cosine is positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\frac{\theta}{2}\ =\ \sqrt{\frac{1\ +\ \frac{4}{5}}{2}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\frac{\theta}{2}\ =\ \sqrt{\frac{9}{10}}\ =\ \frac{3\sqrt{10}}{10}\">\r<BR>\n" );
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document.write( "After rationalizing the denominator.  One last thing:  pie is dessert, pi is the lower case Greek letter denoting the ratio between the circumference and the diameter of a circle.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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