document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=642576>Question 642576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Without using a calculator<BR>\n" );
document.write( "Find 2(theta) given cos(theta) = 5/8 and 0 < theta < pi/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404187 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=404187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Without using a calculator<BR>\n" );
document.write( "Find 2(theta) given cos(theta) = 5/8 and 0 < theta < pi/2<BR>\n" );
document.write( "**<BR>\n" );
document.write( "use x for theta<BR>\n" );
document.write( "cos(x)=5/8<BR>\n" );
document.write( "cos^2(x)=25/64<BR>\n" );
document.write( "sin^2(x)=1-cos^2(x)=1-25/64=64/64-25/64=39/64<BR>\n" );
document.write( "Identity:cos(2x)=cos^2(x)-sin^2(x)<BR>\n" );
document.write( "=25/64-39/64=-14/64=-7/32<BR>\n" );
document.write( "2x=arccos(-7/32)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "check:(w/calculator)<BR>\n" );
document.write( "x=arccos(5/8)=0.89566..<BR>\n" );
document.write( "2x=(2*.89566)=1.7913..<BR>\n" );
document.write( "arccos(-7/32)=1.7913.. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );