document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=749158>Question 749158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sin[tan^-1(5/12)-sin^-1(-1)]\r<BR>\n" );
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document.write( "I need to solve this equation for 0<theta<2pi\r<BR>\n" );
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document.write( "I am familiar with the Product to sum formulas but I do not see where that would play in here because of the arctan(5/12). I know that tan is sin/cos. I tried to see if I can maybe solve it knowing that much, but I cannot seem to figure it out. \r<BR>\n" );
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document.write( "Any help or feedback would be great! Thank you! \r<BR>\n" );
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document.write( "Mayra </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #455864 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=455864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sin[tan^-1(5/12)-sin^-1(-1)] <BR>\n" );
document.write( "let x=the angle whose tan=5/12<BR>\n" );
document.write( "tan(x)=5/12<BR>\n" );
document.write( "hypotenuse=13 (5-12-13 right triangle)<BR>\n" );
document.write( "sin(x)=5/13<BR>\n" );
document.write( "cos(x)=12/13<BR>\n" );
document.write( "..<BR>\n" );
document.write( "let y=the angle whose sin=-1<BR>\n" );
document.write( "sin(y)=-1<BR>\n" );
document.write( "cos(y)=&#8730;(1-sin^2(y))=0<BR>\n" );
document.write( "...<BR>\n" );
document.write( "sin[tan^-1(5/12)-sin^-1(-1)]=sin(x-y)=sin(x)cos(y)-cos(x)sin(y)=5/13*0-12/13*(-1)=12/13<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Check: (with calculator)<BR>\n" );
document.write( "tan(x)=5/12<BR>\n" );
document.write( "x=22.62º<BR>\n" );
document.write( "sin(y) =-1<BR>\n" );
document.write( "y=270º<BR>\n" );
document.write( "x-y=(22.62-270)=-247.38 (in Q3)<BR>\n" );
document.write( "reference angle:67.38º<BR>\n" );
document.write( "sin(x+y)=sin(67.38º)&#8776;0.923..<BR>\n" );
document.write( "exact value=12/13&#8776;0.923..<BR>\n" );
document.write( "          </SPAN>\n" );
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