document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=729916>Question 729916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve: cos^2(theta)+ 2sin(theta)=2 \r<BR>\n" );
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document.write( "Please help. I have no Idea what to do. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446297 by </B><A HREF=/tutors/aboutme.mpl?userid=Leaf+W.><B>Leaf W.(135)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Leaf+W.><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/cgi-bin/show-face.mpl?user=Leaf+W.><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=446297\">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%28theta%29+%2B+2sin%28theta%29+=+2 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29+%2B+2sin%28theta%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29+%2B+cos%5E2%28theta%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29+%2B+cos%5E2%28theta%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (a fundamental trigonometric identity), you can change this to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28theta%29+=+1+-+sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29+=+1+-+sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using basic algebra subtraction on both sides and substitute this into your equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+sin%5E2%28theta%29+%2B+2sin%28theta%29+=+2 ALIGN=MIDDLE  ALT=\"1+-+sin%5E2%28theta%29+%2B+2sin%28theta%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Move everything to the right side: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+sin%5E2%28theta%29+-+2sin%28theta%29+%2B+1 ALIGN=MIDDLE  ALT=\"0+=+sin%5E2%28theta%29+-+2sin%28theta%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Factor: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%28sin%28theta%29+-+1%29%28sin%28theta%29+-+1%29 ALIGN=MIDDLE  ALT=\"0+=+%28sin%28theta%29+-+1%29%28sin%28theta%29+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+-+1+=+0 ALIGN=MIDDLE  ALT=\"sin%28theta%29+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+=+1 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you have to think: for what angles is the sine equal to 1? Well, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. However, it is also 1 at every complete revolution (every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > -- that is, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2+%2B+2pi%2An ALIGN=MIDDLE  ALT=\"pi%2F2+%2B+2pi%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where \"n\" is an integer {think <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3pi%2F2 ALIGN=MIDDLE  ALT=\"-3pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5pi%2F2 ALIGN=MIDDLE  ALT=\"5pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, etc.}). Therefore, the solution to the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+pi%2F2+%2B+2pi%2An ALIGN=MIDDLE  ALT=\"theta+=+pi%2F2+%2B+2pi%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "IF you have a domain restriction in the problem, only include solutions that are within the domain. For example, if you have a restriction of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+theta+%3C+2pi ALIGN=MIDDLE  ALT=\"0+%3C=+theta+%3C+2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then your solution would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+pi%2F2 ALIGN=MIDDLE  ALT=\"theta+=+pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > only because that is the only solution in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2+%2B+2pi%2An ALIGN=MIDDLE  ALT=\"pi%2F2+%2B+2pi%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is between 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;\" >.<BR>\n" );
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document.write( "I hope this helped! Good luck! </SPAN>\n" );
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