document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=742055>Question 742055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is if tan=3/2 and pie is less than or equal to theta, which is less than three pi over two, i have to find the exact value for sin(two theta), cos (two theta), sin(theta/two), and cos (theta/two) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #452266 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=452266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The question is if tan=3/2 and pie is less than or equal to theta, which is less than three pi over two, i have to find the exact value for sin(two theta), cos (two theta), sin(theta/two), and cos (theta/two)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "tan=3/2, (&#960; &#8804; x < 3&#960;/2)(Q3)<BR>\n" );
document.write( "let O=opposite side<BR>\n" );
document.write( "let A=adjacent side<BR>\n" );
document.write( "let H=hypotenuse<BR>\n" );
document.write( "..<BR>\n" );
document.write( "tanx=3/2=O/A<BR>\n" );
document.write( "O=-3, A=-2<BR>\n" );
document.write( "H=&#8730;(O^2+A^2)=&#8730;(9+4)=&#8730;13<BR>\n" );
document.write( "sinx=O/H=-3/&#8730;13<BR>\n" );
document.write( "cosx=A/H=-2/&#8730;13<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(2x)=2sinxcosx=2*(-2/&#8730;13)(-3/&#8730;13)=12/13<BR>\n" );
document.write( "cos(2x)=1-2sin^2x=1-2(-3/&#8730;13)^2=1-18/13=-5/13<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29=sqrt%28%281-cosx%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29=sqrt%28%281-cosx%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "&#8730;((1-(-2/&#8730;13)/2))=&#8730;((1+.5547)/2)=&#8730;(1.5547/2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2F2%29=-sqrt%28%281%2Bcosx%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29=-sqrt%28%281%2Bcosx%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-&#8730;((1+(-2/&#8730;13)/2))=-&#8730;((1-.5547/2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Check with calculator:<BR>\n" );
document.write( "tanx=3/2(in Q3)<BR>\n" );
document.write( "x&#8776;56.31º+180&#8776;236.31º<BR>\n" );
document.write( "2x&#8776;472.62-360&#8776;112.62º<BR>\n" );
document.write( "x/2=118.15º<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin2x=sin(112.62º)&#8776;0.923..<BR>\n" );
document.write( "as computed,12/13&#8776;0.923..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos2x=cos(112.62)=-0.3846..<BR>\n" );
document.write( "as computed,-5/13&#8776;-0.3846..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(x/2)=sin(118.15)&#8776;0.8817..<BR>\n" );
document.write( "as computed,&#8776;0.8817..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(x/2=cos(118.15)=-0.4718..<BR>\n" );
document.write( "as computed,&#8776;-0.4718.. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );