document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=804624>Question 804624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which value of x solves the equation cos x° = sin (20° + x°), where <BR>\n" );
document.write( "0 < x < 90? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #484852 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=484852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "As we work this, keep in mind that sine and cosine are both positive in the first quadrant.\r<BR>\n" );
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document.write( "Use the formula for sine of the sum of two angles:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(\alpha\ +\ \beta)\ =\ \sin\alpha\cos\beta\ +\ \cos\alpha\sin\beta\">\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(20^\circ\ +\ x^\circ)\ =\ \sin20^\circ\cos x^\circ\ +\ \cos20^\circ\sin x^\circ\">\r<BR>\n" );
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document.write( "Hence we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos x^\circ\ =\ \sin20^\circ\cos x^\circ\ +\ \cos20^\circ\sin x^\circ\">  \r<BR>\n" );
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document.write( "A little algebra music, Sammy:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos x^\circ\ -\ \sin20^\circ\cos x^\circ\ =\ \cos20^\circ\sin x^\circ\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos x^\circ\left(1\ -\ \sin20^\circ\right)\ =\ \cos20^\circ\sin x^\circ\">  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\cos x^\circ}{\sin x^\circ}\ =\ \frac{\cos20^\circ}{1\ -\ \sin20^\circ}\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac {\sin x^\circ}{\cos x^\circ}\ =\ \frac  {1\ -\ \sin20^\circ}{\cos20^\circ}\">\r<BR>\n" );
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document.write( "But since sine over cosine is tangent:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \tan^{-1}\left(\frac  {1\ -\ \sin20^\circ}{\cos20^\circ}\right)\">\r<BR>\n" );
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document.write( "The rest is just calculator work.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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