document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=517738>Question 517738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If cos x = -2/3 and x terminates in quadrant 2 find the exact value of cos 2x, sin 2x, and tan 2x... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344975 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=344975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If cos x = -2/3 and x terminates in quadrant 2 find the exact value of cos 2x, sin 2x, and tan 2x<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Cos x terminates in quadrant II where sin>0, cos<0 and tan<0<BR>\n" );
document.write( "You are working with a right triangle where the adjacent side=-2, hypotenuse=3, and opposite side<BR>\n" );
document.write( "=&#8730;[(3^2)-(-2)^2]=&#8730;(9-4)=&#8730;5<BR>\n" );
document.write( "cos x=-2/3 (given)<BR>\n" );
document.write( "sin x=&#8730;5/3<BR>\n" );
document.write( "tan x=sin/cos=(&#8730;5/3)/(-2/3)=-&#8730;5/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos 2x=cos^2x-sin^2x (identity)<BR>\n" );
document.write( "cos 2x=(-2/3)^2-(&#8730;5/3)^2=4/9-5/9=-1/9<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin 2x=2sinx cosx (identity)<BR>\n" );
document.write( "sin 2x=2*&#8730;5/3*2/3=4&#8730;5/9<BR>\n" );
document.write( "..<BR>\n" );
document.write( "tan 2x=2tanx/(1-tan^2x) (identity)<BR>\n" );
document.write( "tan 2x=(2*-&#8730;5/2)/(1-(-&#8730;5/2)^2))=-&#8730;5/(1-5/4)=&#8730;5(-1/4)=-&#8730;5/4 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );