document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=808520>Question 808520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all values of x in the interval [0, 2&#960;] that satisfy the given equation.\r<BR>\n" );
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document.write( "-sin2x = (squreroot 2) cos x\r<BR>\n" );
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document.write( "How do I do this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #487060 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=487060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sin2x+=+sqrt%282%29%2Acosx ALIGN=MIDDLE  ALT=\"-sin2x+=+sqrt%282%29%2Acosx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the trig identity for double-angle formulas<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin2x+=+2sinx%2Acosx ALIGN=MIDDLE  ALT=\"sin2x+=+2sinx%2Acosx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and get<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sinx%2Acosx+=+sqrt%282%29%2Acosx ALIGN=MIDDLE  ALT=\"-2sinx%2Acosx+=+sqrt%282%29%2Acosx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now as long as cos(x) is not equal to zero (to be verified) we can divide both sides of (3) by cos(x) and get<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinx+=+-1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sinx+=+-1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+arcsin%28-1%2Fsqrt%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+arcsin%28-1%2Fsqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or<BR>\n" );
document.write( "(6) x = 225 and 315 degrees. <BR>\n" );
document.write( "Since neither angle has it's cosine equal to zero, the division by cosx in (3) was allowed.<BR>\n" );
document.write( "Answer: x = {225,315} degrees. </SPAN>\n" );
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