document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=687890>Question 687890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a Trigonometry and quadratic question but I couldn't find that as a topic. \r<BR>\n" );
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document.write( "find all solutions, if possible, of the below equation on the interval [0, 2pi]: sin^2x + 3 cos^2 x =0\r<BR>\n" );
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document.write( "also, the given answer is \"No solution\".<BR>\n" );
document.write( "Thank you in advance I need to show my whole class how to do this on Monday, and I'm worried I wont get it right. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425388 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=425388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "Using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2B+3+cos%5E2%28x%29+=0 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2B+3+cos%5E2%28x%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29%2B3%2A%281-sin%5E2%28x%29%29+=+0 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29%2B3%2A%281-sin%5E2%28x%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29%2B3+-+3%2Asin%5E2%28x%29=0 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29%2B3+-+3%2Asin%5E2%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Asin%5E2%28x%29%2B3+=0 ALIGN=MIDDLE  ALT=\"-2%2Asin%5E2%28x%29%2B3+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=2sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"3=2sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2+=+sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"3%2F2+=+sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "Take the square root of both sides.<P><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2F2%29+=+sin%28x%29+=+1.225 ALIGN=MIDDLE  ALT=\"sqrt%283%2F2%29+=+sin%28x%29+=+1.225\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+=+-1.225 ALIGN=MIDDLE  ALT=\"sin%28x%29+=+-1.225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "That can't be true because sin(x) never exceeds 1 or falls below -1.  So the answer is no solution.<BR>\n" );
document.write( "<P>Hope the solution helped.  Sometimes you need more than a solution.  Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.) </SPAN>\n" );
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