document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=671952>Question 671952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for solutions over the interval [0,2pi)\r<BR>\n" );
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document.write( "cot^2 theta= (-5) +4csc theta\r<BR>\n" );
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document.write( "I believe I have solved to the last step which is where I am stuck. \r<BR>\n" );
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document.write( "This is what I have done so far (please forgive all the steps if I do not do them I will get lost and not understand what happened along the way):\r<BR>\n" );
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document.write( "0= (-5) +4csc theta - csc^2 theta +1<BR>\n" );
document.write( "0= (-5) + 1 + 4csc theta - csc ^2 theta<BR>\n" );
document.write( "0= (-4) + 4csc theta - csc^2 theta <BR>\n" );
document.write( "0= -csc^2 theta + 4csc theta - 4<BR>\n" );
document.write( "0= (csc theta -2)(csc theta +2)\r<BR>\n" );
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document.write( "Set both to zero:\r<BR>\n" );
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document.write( "csc theta-2 = 0<BR>\n" );
document.write( "csc theta = 2  (this is where I am stuck...what next?) \r<BR>\n" );
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document.write( "csc theta+2=0<BR>\n" );
document.write( "csc theta = -2 (again stuck here)\r<BR>\n" );
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document.write( "Thank you in advance :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #417975 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=417975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for solutions over the interval [0,2pi) <BR>\n" );
document.write( "cot^2 theta= (-5) +4csc theta <BR>\n" );
document.write( "use x for theta<BR>\n" );
document.write( "cot^2x=-5+4cscx<BR>\n" );
document.write( "cos^2x/sin^2x=-5+4/sinx<BR>\n" );
document.write( "multiply both sides by sin^2x <BR>\n" );
document.write( "cos^2x=-5sin^2x+4sinx<BR>\n" );
document.write( "1-sin^2x=-5sin^2x+4sinx<BR>\n" );
document.write( "4sin^2x-4sinx+1=0<BR>\n" );
document.write( "(2sinx-1)(2sinx-1)=0<BR>\n" );
document.write( "2sinx-1=0<BR>\n" );
document.write( "sinx=1/2<BR>\n" );
document.write( "x=&#960;/6, 5&#960;/6 (multiplicity 2)                                                                                                     </SPAN>\n" );
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