document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=669251>Question 669251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is cos(2theta)  if cos=1/3 and csc<0  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #416328 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=416328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what is cos(2theta) if cos=1/3 and csc<0<BR>\n" );
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document.write( "csc<0 in quadrants III and IV<BR>\n" );
document.write( "cos>0 in quadrants I and IV<BR>\n" );
document.write( "so, we are working with reference angle in quadrant IV<BR>\n" );
document.write( "cosx=1/3=adjacent side/hypotenuse in quadrant IV where cos>0<BR>\n" );
document.write( "opposite side=&#8730;(3^2-1^2)=&#8730;(9-1)=&#8730;8<BR>\n" );
document.write( "sinx=opposite side/hypotenuse=-&#8730;8/3(in quadrant IV where sin<0<BR>\n" );
document.write( "cos2x=cos^2x-sin^2x=1/9-8/9=-7/9<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "cos^-1=1/3<BR>\n" );
document.write( "x&#8776;70.529º<BR>\n" );
document.write( "2x&#8776;141.05756º<BR>\n" );
document.write( "cos2x&#8776;-0.7777..<BR>\n" );
document.write( "-7/9&#8776;-0.7777.. </SPAN>\n" );
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