document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817973>Question 817973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In this problem x means theta\r<BR>\n" );
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document.write( "If tanx= -2/3. And x is in the second quadrant,  use a double angle formula to find sin2x. In which quadrant is 2x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492317 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=492317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If tanx= -2/3. And x is in the second quadrant, use a double angle formula to find sin2x. In which quadrant is 2x?<BR>\n" );
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document.write( "sin(2x)=2sin(x)cos(x)<BR>\n" );
document.write( "reference angle(x)is in quadrant II where sin>0, cos<0, tan<0<BR>\n" );
document.write( "hypotenuse of reference right triangle in quadrant II=&#8730;((2^2)+(3^2))=&#8730;(4+9)=&#8730;13<BR>\n" );
document.write( "sin(x)=2/&#8730;13<BR>\n" );
document.write( "cos(x)=-3/&#8730;13<BR>\n" );
document.write( "sin(2x)=2*2&#8730;13*-3/&#8730;13=-12/13<BR>\n" );
document.write( "..<BR>\n" );
document.write( "calculator check:<BR>\n" );
document.write( "tanx=-2/3<BR>\n" );
document.write( "x&#8776;146.31&#730;(in quadrant II)<BR>\n" );
document.write( "2x&#8776;292.62&#730;(in quadrant IV)<BR>\n" );
document.write( "sin(2x)=sin(292.62)&#8776;-0.923<BR>\n" );
document.write( "exact value as calculated=-12/13&#8776;-0.923<BR>\n" );
document.write( "(2x) is in quadrant IV </SPAN>\n" );
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