document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84895>Question 84895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the exact value of the trigonometric functions listed below.\r<BR>\n" );
document.write( "\n" );
document.write( "cot (135) = is it -1?\r<BR>\n" );
document.write( "\n" );
document.write( "cos(pi/12)....where do I start? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61178 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=61178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28135%29=cos%28135%29%2Fsin%28135%29=%28-sqrt%282%29%2F2%29%2F%28sqrt%282%29%2F2%29=cross%28-sqrt%282%29%2F2%29%2Across%282%2Fsqrt%282%29%29=-1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So you are correct <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28135%29=-1 ALIGN=MIDDLE  ALT=\"cot+%28135%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F12%29=cos%28pi%2F3-pi%2F4%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F12%29=cos%28pi%2F3-pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the argument. Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3-pi%2F4=4pi%2F12-3pi%2F12=1pi%2F12=pi%2F12 ALIGN=MIDDLE  ALT=\"pi%2F3-pi%2F4=4pi%2F12-3pi%2F12=1pi%2F12=pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now use the trig identity:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A-B%29=cos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29 ALIGN=MIDDLE  ALT=\"cos%28A-B%29=cos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F3-pi%2F4%29=cos%28pi%2F3%29cos%28pi%2F4%29%2Bsin%28pi%2F3%29sin%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F3-pi%2F4%29=cos%28pi%2F3%29cos%28pi%2F4%29%2Bsin%28pi%2F3%29sin%28pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=pi%2F3 ALIGN=MIDDLE  ALT=\"A=pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=pi%2F4 ALIGN=MIDDLE  ALT=\"B=pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now using the unit circle, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F3%29=1%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F3%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F4%29=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F4%29=sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F3%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%28pi%2F3%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F3%29=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sin%28pi%2F3%29=sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F3-pi%2F4%29=%281%2F2%29%28sqrt%282%29%2F2%29%2B%28sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute each trig function with it's corresponding expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F3-pi%2F4%29=sqrt%282%29%2F4%2Bsqrt%286%29%2F4 ALIGN=MIDDLE  ALT=\"cos%28pi%2F3-pi%2F4%29=sqrt%282%29%2F4%2Bsqrt%286%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F3-pi%2F4%29=%28sqrt%282%29%2Bsqrt%286%29%29%2F4 ALIGN=MIDDLE  ALT=\"cos%28pi%2F3-pi%2F4%29=%28sqrt%282%29%2Bsqrt%286%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F12%29=%28sqrt%282%29%2Bsqrt%286%29%29%2F4 ALIGN=MIDDLE  ALT=\"cos%28pi%2F12%29=%28sqrt%282%29%2Bsqrt%286%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );