document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007348>Question 1007348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose cos(u)= 5/13, and sin(u) is negative. Find sin(u-pi), cos(u-pi), sin(u-pi/2), cos(u-pi/2)\r<BR>\n" );
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document.write( "I tried solving this question but I could not get the right answer. Here are the step I tried for solving this problem.\r<BR>\n" );
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document.write( "cos(u) 5/13 = x/r\r<BR>\n" );
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document.write( "Use pythagoream theorem to find sin(u)<BR>\n" );
document.write( "x=5, r=13\r<BR>\n" );
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document.write( "r^2=x^2+y^2<BR>\n" );
document.write( "13^2=5^2+y^2<BR>\n" );
document.write( "169=25+y^2<BR>\n" );
document.write( "sqrt(144)=y^2 ==> y=12\r<BR>\n" );
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document.write( "sin(u)= -12/13\r<BR>\n" );
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document.write( "sin(u-pi)<BR>\n" );
document.write( "=(-12/13)-(0/1)<BR>\n" );
document.write( "=(-12/13)-0 ==> -12/13\r<BR>\n" );
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document.write( "cos(u-pi)<BR>\n" );
document.write( "=(5/13)-(1/0)<BR>\n" );
document.write( "=undefined\r<BR>\n" );
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document.write( "sin(u-pi/2)<BR>\n" );
document.write( "=(-12/13)-(sqrt(2)/2)<BR>\n" );
document.write( "=(-12-sqrt(2))/11\r<BR>\n" );
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document.write( "cos(u-pi/2)<BR>\n" );
document.write( "=(5/13)-(sqrt(2)/2)<BR>\n" );
document.write( "=(5-sqrt(2))/11<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623282 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=623282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cos(u) = 5/13<BR>\n" );
document.write( "sin(u) = -12/13 (found from the pythagorean theorem)<BR>\n" );
document.write( "angle u is in quadrant 4\r<BR>\n" );
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document.write( "Use <a  rel=nofollow HREF= \"http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf\">this page</a> to look at the identities used. In this case, I'm going to use these two identities\r<BR>\n" );
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document.write( "sin(x - y) = sin(x)cos(y) - cos(x)sin(y)<BR>\n" );
document.write( "cos(x - y) = cos(x)cos(y) + sin(x)sin(y)\r<BR>\n" );
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document.write( "those identities are found in the \"Sum and Difference Formulas\" section on page 2 of the reference sheet.\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "sin(u - pi) = sin(u)cos(pi) - cos(u)sin(pi)<BR>\n" );
document.write( "sin(u - pi) = sin(u)(-1) - cos(u)(0)<BR>\n" );
document.write( "sin(u - pi) = -sin(u)<BR>\n" );
document.write( "sin(u - pi) = -(-12/13)<BR>\n" );
document.write( "sin(u - pi) = 12/13\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "cos(u - pi) = cos(u)*cos(pi) + sin(u)*sin(pi)<BR>\n" );
document.write( "cos(u - pi) = cos(u)*(-1) + sin(u)*0<BR>\n" );
document.write( "cos(u - pi) = -cos(u)<BR>\n" );
document.write( "cos(u - pi) = -5/13\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "sin(u - pi/2) = sin(u)cos(pi/2) - cos(u)sin(pi/2)<BR>\n" );
document.write( "sin(u - pi/2) = sin(u)(0) - cos(u)(1)<BR>\n" );
document.write( "sin(u - pi/2) = -cos(u)<BR>\n" );
document.write( "sin(u - pi/2) = -5/13\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "cos(u - pi/2) = cos(u)*cos(pi/2) + sin(u)*sin(pi/2)<BR>\n" );
document.write( "cos(u - pi/2) = cos(u)*(0) + sin(u)*1<BR>\n" );
document.write( "cos(u - pi/2) = sin(u)<BR>\n" );
document.write( "cos(u - pi/2) = -12/13 </SPAN>\n" );
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