document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=600688>Question 600688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hey please help me with this problem,and if possible can you show me the work that leads to the answer. thank you very much\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if cot x = 5/12 and cos x > 0 find csc </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379433 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=379433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cot(x) = 5/12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cot^2(x) = (5/12)^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cot^2(x) = 25/144\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now use the identity 1+cot^2(x) = csc^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1+cot^2(x) = csc^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1+25/144 = csc^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "169/144 = csc^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "csc^2(x) = 169/144\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "csc(x) = sqrt(169/144) ... See <font color=\"red\">note</font> below\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "csc(x) = sqrt(169)/sqrt(144)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "csc(x) = 13/12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=\"red\">Note</font>: Because cos(x) > 0 and cot(x) = cos(x)/sin(x), this means that sin(x) > 0 as well (to keep cot(x) positive). This forces csc(x) > 0 (because csc(x) = 1/sin(x))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==========================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=\"red\">Answer:</font> So the answer is csc(x) = 13/12 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );