document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=870615>Question 870615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for solutions over the interval [0, 360). Give solutions to the nearest tenth as appropriate. \r<BR>\n" );
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document.write( "Cos^2(theta) = sin^2(theta) + 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #525008 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=525008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First solve for theta\r<BR>\n" );
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document.write( "cos^2(theta) = sin^2(theta) + 1<BR>\n" );
document.write( "cos^2(theta) - sin^2(theta) = 1<BR>\n" );
document.write( "cos(2theta) = 1<BR>\n" );
document.write( "2theta = arcos(1)<BR>\n" );
document.write( "2theta = 0+360*n<BR>\n" );
document.write( "2theta = 360*n<BR>\n" );
document.write( "theta = 360*n/2<BR>\n" );
document.write( "theta = 180n\r<BR>\n" );
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document.write( "So theta = 180n generates all of the solutions for theta where n is an integer.\r<BR>\n" );
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document.write( "If n = 0, then<BR>\n" );
document.write( "theta = 180n<BR>\n" );
document.write( "theta = 180*0<BR>\n" );
document.write( "theta = 0\r<BR>\n" );
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document.write( "If n = 1, then<BR>\n" );
document.write( "theta = 180*n<BR>\n" );
document.write( "theta = 180*1<BR>\n" );
document.write( "theta = 180\r<BR>\n" );
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document.write( "If n = 2, then<BR>\n" );
document.write( "theta = 180*n<BR>\n" );
document.write( "theta = 180*2<BR>\n" );
document.write( "theta = 360 ... toss this solution since it's not in the interval [0, 360)\r<BR>\n" );
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document.write( "The only two solutions are <font color=\"red\">theta = 0, theta = 180</font> (both in degrees)<BR>\n" );
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