document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967994>Question 967994</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sin(x)= -4/5, on the interval (pi,3pi/2) find the exact value of tan2(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591651 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=591651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If sin(x)= -4/5, on the interval (pi,3pi/2) find the exact value of tan2(x)<BR>\n" );
document.write( "reference angle x is in quadrant III where cos<0, sin<0<BR>\n" );
document.write( "sinx=-4/5<BR>\n" );
document.write( "cosx=-3/5<BR>\n" );
document.write( "sin(2x)=2sinxcosx=2*-4/5*-3/5=24/25<BR>\n" );
document.write( "cos(2x)=cos^2(x)-sin(^2(x)=9/25-16/25=-7/25<BR>\n" );
document.write( "tan(2x)=sin(2x)/cos(2x)=-24/7<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "sinx=-4/5 (Q3)<BR>\n" );
document.write( "x=233.13<BR>\n" );
document.write( "2x=106.26<BR>\n" );
document.write( "tan(2x)=tan(466.26)&#8776;3.4286<BR>\n" );
document.write( "exact value as computed above=-24/7&#8776;3.4386 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );