document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009676>Question 1009676</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions in the interval [0, 2&#960;). (Enter your answers as a comma-separated list.) \r<BR>\n" );
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document.write( "sin(&#952;) cos(3&#952;) + cos(&#952;) sin(3&#952;) = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625301 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52793)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=625301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29%2Acos%283%2Atheta%29+%2B+cos%28theta%29%2Asin%283%2Atheta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29%2Acos%283%2Atheta%29+%2B+cos%28theta%29%2Asin%283%2Atheta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Use the formula \r<BR>\n" );
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document.write( "sin(alpha)*cos(beta) + cos(alpha)*sin(beta) = sin(alpha+beta)\r<BR>\n" );
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document.write( "It is the formula for sine of the sum of arguments - one of fundamental formula of Trigonometry.\r<BR>\n" );
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document.write( "See, for example, the lesson <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A> in this site. \r<BR>\n" );
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document.write( "When you apply this formula to the left side of your equation, you will get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%284%2Atheta%29 ALIGN=MIDDLE  ALT=\"sin%284%2Atheta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The general solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Atheta ALIGN=MIDDLE  ALT=\"4%2Atheta\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2Api ALIGN=MIDDLE  ALT=\"k%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >, k = 0, +/-1, +/-2, . . . \r<BR>\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2A%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"k%2A%28pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, k = 0, +/-1, +/-2, . . . \r<BR>\n" );
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document.write( "For the given interval [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >) the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2A%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"k%2A%28pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for k = 0, 1, 2, . . . , 7.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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