document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920256>Question 920256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I express sin(x+y+z) in terms of cosines and sines of x, y and z?\r<BR>\n" );
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document.write( "I know that you can express<BR>\n" );
document.write( "sin(x+y) into<BR>\n" );
document.write( "=sinxcosy+cosxsiny<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558245 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=558245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+=+x%2By ALIGN=MIDDLE  ALT=\"Q+=+x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You don't have to use Q. Just any other variable not being used.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%2Bz%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will then turn into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28Q%2Bz%29 ALIGN=MIDDLE  ALT=\"sin%28Q%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > after you replace \"x+y\" with \"Q\" (the substitution is valid based on the definition we made above).\r<BR>\n" );
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document.write( "Expand out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28Q%2Bz%29 ALIGN=MIDDLE  ALT=\"sin%28Q%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28Q%2Bz%29+=+sin%28Q%29cos%28z%29%2Bcos%28Q%29sin%28z%29 ALIGN=MIDDLE  ALT=\"sin%28Q%2Bz%29+=+sin%28Q%29cos%28z%29%2Bcos%28Q%29sin%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28Q%29cos%28z%29%2Bcos%28Q%29sin%28z%29 ALIGN=MIDDLE  ALT=\"sin%28Q%29cos%28z%29%2Bcos%28Q%29sin%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Next, replace every Q with \"x+y\" to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28Q%29cos%28z%29%2Bcos%28Q%29sin%28z%29 ALIGN=MIDDLE  ALT=\"sin%28Q%29cos%28z%29%2Bcos%28Q%29sin%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%29cos%28z%29%2Bcos%28x%2By%29sin%28z%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%29cos%28z%29%2Bcos%28x%2By%29sin%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > replace every Q with \"x+y\"\r<BR>\n" );
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document.write( "The next step is to expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2By%29 ALIGN=MIDDLE  ALT=\"cos%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%29+=+sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%29+=+sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2By%29+=+cos%28x%29cos%28y%29-sin%28x%29sin%28y%29 ALIGN=MIDDLE  ALT=\"cos%28x%2By%29+=+cos%28x%29cos%28y%29-sin%28x%29sin%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which you will use to replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2By%29 ALIGN=MIDDLE  ALT=\"cos%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%29cos%28z%29%2Bcos%28x%2By%29sin%28z%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%29cos%28z%29%2Bcos%28x%2By%29sin%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%29cos%28z%29%2Bcos%28x%2By%29sin%28z%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%29cos%28z%29%2Bcos%28x%2By%29sin%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29%29cos%28z%29%2Bcos%28x%2By%29sin%28z%29 ALIGN=MIDDLE  ALT=\"%28sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29%29cos%28z%29%2Bcos%28x%2By%29sin%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29 ALIGN=MIDDLE  ALT=\"sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29%29cos%28z%29%2B%28cos%28x%29cos%28y%29-sin%28x%29sin%28y%29%29sin%28z%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2By%29 ALIGN=MIDDLE  ALT=\"cos%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29cos%28y%29-sin%28x%29sin%28y%29 ALIGN=MIDDLE  ALT=\"cos%28x%29cos%28y%29-sin%28x%29sin%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29cos%28y%29cos%28z%29%2Bcos%28x%29sin%28y%29cos%28z%29%2Bcos%28x%29cos%28y%29sin%28z%29-sin%28x%29sin%28y%29sin%28z%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2By%2Bz%29 ALIGN=MIDDLE  ALT=\"sin%28x%2By%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > expands out into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29cos%28y%29cos%28z%29%2Bcos%28x%29sin%28y%29cos%28z%29%2Bcos%28x%29cos%28y%29sin%28z%29-sin%28x%29sin%28y%29sin%28z%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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