document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=821438>Question 821438</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find cos2x,sin2x , and tan2x if sinx=-12/13 and x terminates in quadrant IV . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #494141 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=494141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find cos2x,sin2x , and tan2x if sinx=-12/13 and x terminates in quadrant IV .<BR>\n" );
document.write( "Identities:<BR>\n" );
document.write( "cos2x=cos^2x-sin^2x<BR>\n" );
document.write( "sin2x=2sinxcosx<BR>\n" );
document.write( "tan2x=(2tanx)/(1-tan^2x)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sinx=-12/13<BR>\n" );
document.write( "you are working with a (5-12-13) reference right triangle in quadrant IV where sin<0,cos>0,tan<0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sinx=-12/13 (given)<BR>\n" );
document.write( "cosx=5/13<BR>\n" );
document.write( "tanx=-12/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos2x=cos^2x-sin^2x=25/169-144/69=-119/169<BR>\n" );
document.write( "sin2x=2sinxcosx=2*(-12/13)*(5/13)=-120/169<BR>\n" );
document.write( "tan2x=(2tanx)/(1-tan^2x)<BR>\n" );
document.write( "=2(-12/5)/(1-(144/25))=(-24/5)/(-119/25)=(-24/5)(25/119)=120/119<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );