document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=870609>Question 870609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions in the interval [0, 2pi) for the equation sin^2&#952;=cos^2&#952;-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #525009 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=525009\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to use the variable x instead of the variable &#952;\r<BR>\n" );
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document.write( "Solve for x\r<BR>\n" );
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document.write( "sin^2(x)=cos^2(x)-1<BR>\n" );
document.write( "sin^2(x)-cos^2(x) = -1<BR>\n" );
document.write( "-1(-sin^2(x)+cos^2(x)) = -1<BR>\n" );
document.write( "-sin^2(x)+cos^2(x) = 1<BR>\n" );
document.write( "cos^2(x)-sin^2(x) = 1<BR>\n" );
document.write( "cos(2x) = 1<BR>\n" );
document.write( "2x = arccos(1)<BR>\n" );
document.write( "2x = 0+2pi*n<BR>\n" );
document.write( "2x = 2pi*n<BR>\n" );
document.write( "x = 2pi*n/2<BR>\n" );
document.write( "x = pi*n\r<BR>\n" );
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document.write( "All solutions for x are generated by x = pi*n where n is an integer\r<BR>\n" );
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document.write( "If n = -1, then<BR>\n" );
document.write( "x = pi*n<BR>\n" );
document.write( "x = pi*(-1)<BR>\n" );
document.write( "x = -pi ... not in the interval [0, 2pi), so we ignore it\r<BR>\n" );
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document.write( "If n = 0, then<BR>\n" );
document.write( "x = pi*n<BR>\n" );
document.write( "x = pi*0<BR>\n" );
document.write( "x = 0\r<BR>\n" );
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document.write( "If n = 1, then<BR>\n" );
document.write( "x = pi*n<BR>\n" );
document.write( "x = pi*1<BR>\n" );
document.write( "x = pi\r<BR>\n" );
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document.write( "If n = 2, then<BR>\n" );
document.write( "x = pi*n<BR>\n" );
document.write( "x = pi*2<BR>\n" );
document.write( "x = 2pi ... not in the interval [0, 2pi), so we ignore it\r<BR>\n" );
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document.write( "The only two solutions are <font color=\"red\">x = 0, x = pi</font> (both in radians)<BR>\n" );
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