document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180471>Question 1180471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If cos t = 3/5 and the terminal point for t is in quadrant IV, find cot t + csc t. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810146 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=810146\">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=cos+%28t%29+=+3%2F5%7D%7D%0D%0A%0D%0A+and+the+terminal+point+for+%7B%7B%7Bt ALIGN=MIDDLE  ALT=\"cos+%28t%29+=+3%2F5%7D%7D%0D%0A%0D%0A+and+the+terminal+point+for+%7B%7B%7Bt\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in quadrant IV, \r<BR>\n" );
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document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28+t%29+%2B+csc+%28t%29 ALIGN=MIDDLE  ALT=\"cot%28+t%29+%2B+csc+%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "recall:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28t%29+=+adj%2Fhyp ALIGN=MIDDLE  ALT=\"cos+%28t%29+=+adj%2Fhyp\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28t%29+=+3%2F5%7D%7D=%3E%7B%7B%7B+adj=3 ALIGN=MIDDLE  ALT=\"cos+%28t%29+=+3%2F5%7D%7D=%3E%7B%7B%7B+adj=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hyp=5%7D%7D%0D%0A%0D%0Athen+%7B%7B%7Bopp=sqrt%285%5E2-3%5E2%29 ALIGN=MIDDLE  ALT=\"hyp=5%7D%7D%0D%0A%0D%0Athen+%7B%7B%7Bopp=sqrt%285%5E2-3%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opp=sqrt%2825-9%29 ALIGN=MIDDLE  ALT=\"opp=sqrt%2825-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opp=sqrt%2816%29 ALIGN=MIDDLE  ALT=\"opp=sqrt%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opp=4 ALIGN=MIDDLE  ALT=\"opp=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opp=-4 ALIGN=MIDDLE  ALT=\"opp=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28t%29=4%2F5 ALIGN=MIDDLE  ALT=\"sin%28t%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28t%29=-4%2F5 ALIGN=MIDDLE  ALT=\"sin%28t%29=-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " since given that the terminal point for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in quadrant IV, sine is negative, so we will use<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28t%29=-4%2F5 ALIGN=MIDDLE  ALT=\"sin%28t%29=-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using identities <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28+t%29+=cos+%28t%29%2Fsin%28t%29 ALIGN=MIDDLE  ALT=\"cot%28+t%29+=cos+%28t%29%2Fsin%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc+%28t%29=1%2Fsin%28t%29 ALIGN=MIDDLE  ALT=\"csc+%28t%29=1%2Fsin%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28+t%29+%2B+csc+%28t%29=cos+%28t%29%2Fsin%28t%29+%2B1%2Fsin%28t%29 ALIGN=MIDDLE  ALT=\"cot%28+t%29+%2B+csc+%28t%29=cos+%28t%29%2Fsin%28t%29+%2B1%2Fsin%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...substitute values above\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28+t%29+%2B+csc+%28t%29=%283%2F5%29%2F+%28-4%2F5%29%2B1%2F%28-4%2F5%29 ALIGN=MIDDLE  ALT=\"cot%28+t%29+%2B+csc+%28t%29=%283%2F5%29%2F+%28-4%2F5%29%2B1%2F%28-4%2F5%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=cot%28+t%29+%2B+csc+%28t%29=%283%2F5%2B1%29%2F%28-4%2F5%29 ALIGN=MIDDLE  ALT=\"cot%28+t%29+%2B+csc+%28t%29=%283%2F5%2B1%29%2F%28-4%2F5%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=cot%28+t%29+%2B+csc+%28t%29=%288%2F5%29%2F%28-4%2F5%29 ALIGN=MIDDLE  ALT=\"cot%28+t%29+%2B+csc+%28t%29=%288%2F5%29%2F%28-4%2F5%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=cot%28+t%29+%2B+csc+%28t%29=-2 ALIGN=MIDDLE  ALT=\"cot%28+t%29+%2B+csc+%28t%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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