document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130301>Question 1130301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph one period the function y = 3 csc(1/2)x Show the asymptotes and the extrema.\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746989 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=746989\">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=y+=+3csc%28x%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+3csc%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Show the asymptotes and the extrema.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%281%2Fsin%28x%2F2%29%29 ALIGN=MIDDLE  ALT=\"y+=+3%281%2Fsin%28x%2F2%29%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=+graph%28+600%2C+600%2C+-30%2C+30%2C+-10%2C+10%2C3%281%2Fsin%28x%2F2%29%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-30%2C+30%2C+-10%2C+10%2C3%281%2Fsin%28x%2F2%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "vertical asymptote <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2pi%2An ALIGN=MIDDLE  ALT=\"x=2pi%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >  where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an integer\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3csc%28x%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+3csc%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is asymptotic to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3+csc%28x%2F2%29+ ALIGN=MIDDLE  ALT=\"y+=+3+csc%28x%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is asymptotic to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2pi+%282n+%2B+1%29 ALIGN=MIDDLE  ALT=\"x+=+2pi+%282n+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3+csc%28x%2F2%29+ ALIGN=MIDDLE  ALT=\"y+=+3+csc%28x%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is asymptotic to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4pi%2An ALIGN=MIDDLE  ALT=\"x+=+4pi%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "asymptote: \r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=0 ALIGN=MIDDLE  ALT=\"n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2pi+%282%2A0+%2B+1%29 ALIGN=MIDDLE  ALT=\"x+=+2pi+%282%2A0+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2pi+ ALIGN=MIDDLE  ALT=\"x+=+2pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=0 ALIGN=MIDDLE  ALT=\"n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4pi%2A0 ALIGN=MIDDLE  ALT=\"x+=+4pi%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2pi+%282%2A1+%2B+1%29 ALIGN=MIDDLE  ALT=\"x+=+2pi+%282%2A1+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6pi+ ALIGN=MIDDLE  ALT=\"x+=+6pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4pi%2A1 ALIGN=MIDDLE  ALT=\"x+=+4pi%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4pi ALIGN=MIDDLE  ALT=\"x=4pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and so on\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28+600%2C+600%2C+-30%2C+30%2C+-10%2C+10%2C%0D%0Aline%284pi%2C10%2C4pi%2C-10%29%2Cline%282pi%2C10%2C2pi%2C-10%29%2Cgreen%28line%280%2C10%2C0%2C-10%29%29%2C%0D%0Aline%288pi%2C10%2C8pi%2C-10%29%2Cline%286pi%2C10%2C6pi%2C-10%29%2Cline%28-6pi%2C10%2C-6pi%2C-10%29%2C%0D%0Aline%28-4pi%2C10%2C-4pi%2C-10%29%2Cline%28-2pi%2C10%2C-2pi%2C-10%29%2Cline%28-8pi%2C10%2C-8pi%2C-10%29%2C%0D%0Agraph%28+600%2C+600%2C+-30%2C+30%2C+-10%2C+10%2C3%281%2Fsin%28x%2F2%29%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "period <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Fb ALIGN=MIDDLE  ALT=\"2pi%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F2 ALIGN=MIDDLE  ALT=\"b=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F%281%2F2%29=4pi ALIGN=MIDDLE  ALT=\"2pi%2F%281%2F2%29=4pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "amplitude: none\r<BR>\n" );
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document.write( "max<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3csc%28x%2F2%29+=+-3 ALIGN=MIDDLE  ALT=\"3csc%28x%2F2%29+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4pi%2A+n+-+pi ALIGN=MIDDLE  ALT=\"x+=+4pi%2A+n+-+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > for integer<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n ALIGN=MIDDLE  ALT=\"+n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "min<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3csc%28x%2F2%29+=+3 ALIGN=MIDDLE  ALT=\"3csc%28x%2F2%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4pi%2An++%2B+pi ALIGN=MIDDLE  ALT=\"x+=+4pi%2An++%2B+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > for integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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