document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825816>Question 825816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If cos(theta)=4/5, 0<(theta)<pi/2, <BR>\n" );
document.write( "find the exact value of<BR>\n" );
document.write( "a) Sin 2(theta)<BR>\n" );
document.write( "b) Sin 4(theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497645 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=497645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If cos(theta)=4/5, 0<(theta) find the exact value of<BR>\n" );
document.write( "a) Sin 2(theta)<BR>\n" );
document.write( "b) Sin 4(theta)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "cosx=4/5 (working with a (3-4-5) reference right triangle)<BR>\n" );
document.write( "sinx=3/4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "a)sin2x=2sinxcosx=2*4/5*3/5=24/25<BR>\n" );
document.write( "cos2x=&#8730;(1-sin^2(2x))=&#8730;(1-(576/625))=&#8730;(1-(576/625))=&#8730;(49/625)=7/25<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b)sin4x=2sin2xcos2x=2*24/25*7/25=336/625<BR>\n" );
document.write( "..<BR>\n" );
document.write( "calculator check:<BR>\n" );
document.write( "cosx=4/5<BR>\n" );
document.write( "x&#8776;36.87&#730;<BR>\n" );
document.write( "4x&#8776;147.48&#730;<BR>\n" );
document.write( "sin4x&#8776;sin(147.48&#730;)&#8776;0.5376..<BR>\n" );
document.write( "exact value as calculated=336/625&#8776;0.5376.. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );