document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615276>Question 615276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find solutions in the interval (0,2pi)cos^2x=1-sinx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387088 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=387088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28x%29=1-sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29=1-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28x%29+=+1+-+sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29+=+1+-+sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to change the equation into an \"all-sin\" equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+sin%5E2%28x%29=1-sin%28x%29 ALIGN=MIDDLE  ALT=\"1+-+sin%5E2%28x%29=1-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Next we solve for sin(x). This equation is quadratic in terms of sin(x) so we want one side to be zero. Subtracting 1 and adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+sin%5E2%28x%29+-+sin%28x%29 ALIGN=MIDDLE  ALT=\"0+=+sin%5E2%28x%29+-+sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor. The GCF is sin(x):<BR>\n" );
document.write( "0 = sin(x)(sin(x) - 1)<BR>\n" );
document.write( "Use the Zero Product Property:<BR>\n" );
document.write( "sin(x) = 0 or sin(x) - 1 = 0<BR>\n" );
document.write( "Solving the second equation we get:<BR>\n" );
document.write( "sin(x) = 0 or sin(x) = 1<br><BR>\n" );
document.write( "Now that we have solved for sin(x), we can solve for x. Sin values of 0 and 1 are special angle values. So we do not need a calculator. From the special angles we know that...<BR>\n" );
document.write( "For sin(x) = 0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0+%2B+2%2Api%2An ALIGN=MIDDLE  ALT=\"x+=+0+%2B+2%2Api%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi+%2B+2%2Api%2An ALIGN=MIDDLE  ALT=\"x+=+pi+%2B+2%2Api%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For sin(x) = 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi%2F2+%2B+2%2Api%2An ALIGN=MIDDLE  ALT=\"x+=+pi%2F2+%2B+2%2Api%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "From these three equations we can find all the x's that are in the specified interval.<BR>\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0+%2B+2%2Api%2An ALIGN=MIDDLE  ALT=\"x+=+0+%2B+2%2Api%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<BR>\n" );
document.write( "We get no solutions. (Did you post the interval correctly? I ask because often there is a bracket, not a parenthesis, on one or maybe both ends of the interval. A bracket at one of end of an interval means \"including the number at that end\". A parenthesis means \"not including....\" Since you posted parentheses at both ends, 0 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > are excluded. If either one of these is supposed to be included, then this equation says they would be a solution in the interval.)<br><BR>\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi+%2B+2%2Api%2An ALIGN=MIDDLE  ALT=\"x+=+pi+%2B+2%2Api%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<BR>\n" );
document.write( "we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi ALIGN=MIDDLE  ALT=\"x+=+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the only solution within the specified interval.<br><BR>\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi%2F2+%2B+2%2Api%2An ALIGN=MIDDLE  ALT=\"x+=+pi%2F2+%2B+2%2Api%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<BR>\n" );
document.write( "we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi%2F2 ALIGN=MIDDLE  ALT=\"x+=+pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the only solution within the specified interval.<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );