document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636444>Question 636444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if sin theta = radical 5 over 3 , then what does cos 2 theta equal ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401199 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=401199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We will be using the cos(2x) formula for this. There are three variations of this formula:<ul><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29+=+cos%5E2%28x%29-sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"cos%282x%29+=+cos%5E2%28x%29-sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29+=+2cos%5E2%28x%29-1 ALIGN=MIDDLE  ALT=\"cos%282x%29+=+2cos%5E2%28x%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29+=+1-2sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"cos%282x%29+=+1-2sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul>Any one of these three can be used. Often, choosing a particular one for a particular problem will make it easier. In this problem, since we already have sin(x), using the \"all-sin\" version, the third one, will make this problem easier. (The other two variations require that we have cos(x) which we do not yet have.)<br><BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282theta%29+=+1+-+2sin%5E2%28theta%29+=+1+-+2%28sqrt%285%29%2F3%29%5E2+=+1+-+2%285%2F9%29+=+1+-+10%2F9+=+9%2F9+-+10%2F9+=+-1%2F9 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "P.S. It is not good to use the phrase \"radical 5\", even if your teacher uses it. Radicals are used to express <i>all</i> kinds of roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+5%29 ALIGN=MIDDLE  ALT=\"root%283%2C+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C+5%29 ALIGN=MIDDLE  ALT=\"root%284%2C+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%285%2C+5%29 ALIGN=MIDDLE  ALT=\"root%285%2C+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "\"Radical 5\" could mean <i>any</i> of these. I had to guess that you meant square root. For square roots, say \"square root\" or just \"sqrt\". In the future, please post your questions in clear, unambiguous ways. Tutors are less likely to help if they are not even sure what the problem is. </SPAN>\n" );
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