document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154166>Question 1154166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate Sec 660degrees + Cot 405degrees without using a calculator. Please show steps thanks you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776545 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=776545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28+660%29+%2B+cot+%28405%29 ALIGN=MIDDLE  ALT=\"sec%28+660%29+%2B+cot+%28405%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........express <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28+660%29 ALIGN=MIDDLE  ALT=\"sec%28+660%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  with sin and cos\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%28+660%29+%2B+cot%28405%29 ALIGN=MIDDLE  ALT=\"1%2Fcos%28+660%29+%2B+cot%28405%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..use identity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=sin%2890-x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29=sin%2890-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..since your <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=660 ALIGN=MIDDLE  ALT=\"x=660\"   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=1%2Fsin%2890-660%29+%2B+cot%28405%29 ALIGN=MIDDLE  ALT=\"1%2Fsin%2890-660%29+%2B+cot%28405%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=1%2Fsin%28-570%29+%2B+cot%28405%29 ALIGN=MIDDLE  ALT=\"1%2Fsin%28-570%29+%2B+cot%28405%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........use the following property : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28-x+t%29=-+sin+%28x+%29 ALIGN=MIDDLE  ALT=\"sin+%28-x+t%29=-+sin+%28x+%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=-1%2Fsin%28570%29+%2B+cot%28405%29 ALIGN=MIDDLE  ALT=\"-1%2Fsin%28570%29+%2B+cot%28405%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28570%29 ALIGN=MIDDLE  ALT=\"sin%28570%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......... apply the periodicity of sin : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28570%29=sin%28x%2B360%2Ak%29=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28570%29=sin%28x%2B360%2Ak%29=sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28570%29+=sin%28210%29+ ALIGN=MIDDLE  ALT=\"sin%28570%29+=sin%28210%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=-1%2Fsin%28210%29+%2B+cot%28405%29 ALIGN=MIDDLE  ALT=\"-1%2Fsin%28210%29+%2B+cot%28405%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >................rewrite the angles for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28405=360%2B45%29 ALIGN=MIDDLE  ALT=\"cot%28405=360%2B45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%2845%29 ALIGN=MIDDLE  ALT=\"cot%2845%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=-1%2Fsin%28210%29+%2B+cot%2845%29 ALIGN=MIDDLE  ALT=\"-1%2Fsin%28210%29+%2B+cot%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28210+%29 ALIGN=MIDDLE  ALT=\"sin+%28210+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28180+%2B30+%29 ALIGN=MIDDLE  ALT=\"sin+%28180+%2B30+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using the summation identity : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28x%2By+%29=+sin++%28x+%29+cos+%28y+%29%2B+cos+%28x+%29+sin+%28y+%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2By+%29=+sin++%28x+%29+cos+%28y+%29%2B+cos+%28x+%29+sin+%28y+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28180+%2B30+%29=+sin++%28180+%29+cos+%2830+%29%2B+cos+%28180+%29+sin+%2830+%29 ALIGN=MIDDLE  ALT=\"sin+%28180+%2B30+%29=+sin++%28180+%29+cos+%2830+%29%2B+cos+%28180+%29+sin+%2830+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now use the following trivial identities:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin++%28180+%29=0 ALIGN=MIDDLE  ALT=\"sin++%28180+%29=0\"   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=cos+%28180+%29=-1 ALIGN=MIDDLE  ALT=\"cos+%28180+%29=-1\"   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+%2830+%29=1%2F2 ALIGN=MIDDLE  ALT=\"sin+%2830+%29=1%2F2\"   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=cos+%2830+%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos+%2830+%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28180+%2B30+%29=+0%2A++%28sqrt%283%29%2F2+%29%2B+%28-1+%29+%281%2F2+%29=-1%2F2 ALIGN=MIDDLE  ALT=\"sin+%28180+%2B30+%29=+0%2A++%28sqrt%283%29%2F2+%29%2B+%28-1+%29+%281%2F2+%29=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%2845%29=cos%2845%29%2Fsin%2845%29=%281%2Fsqrt%282%29%29+%2F%281%2Fsqrt%282%29%29=1+ ALIGN=MIDDLE  ALT=\"cot%2845%29=cos%2845%29%2Fsin%2845%29=%281%2Fsqrt%282%29%29+%2F%281%2Fsqrt%282%29%29=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, you have:\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28-1%2F2%29+%2B+1 ALIGN=MIDDLE  ALT=\"-1%2F%28-1%2F2%29+%2B+1\"   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=2+%2B+1 ALIGN=MIDDLE  ALT=\"2+%2B+1\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   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=sec%28+660%29+%2B+cot+%28405%29=3 ALIGN=MIDDLE  ALT=\"sec%28+660%29+%2B+cot+%28405%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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