document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=454698>Question 454698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the period and 2 consecutive asymptotes of the graph:\<BR>\n" );
document.write( "a) y= csc x/3\r<BR>\n" );
document.write( "\n" );
document.write( "b) y= 3 cot pi(x)/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #312274 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=312274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> State the period and 2 consecutive asymptotes of the graph:\<BR>\n" );
document.write( "a) y= csc x/3 <BR>\n" );
document.write( "b) y= 3 cot pi(x)/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "a) Standard form for csc function: y=Asec(Bx-C), with period =2&#960;/B, phase-shift=C/B, A=multiplier which stretches curve vertically.<BR>\n" );
document.write( "For given function, y= csc x/3, A=1, phase-shift=0<BR>\n" );
document.write( "period=2&#960;/B=2&#960;/(1/3)=6&#960;<BR>\n" );
document.write( "Asymptotes: x=0 and x=3&#960; (Note that at 0, and every half period thereafter, sin x, the reciprocal of csc x, is approaching 0, so csc x is approaching infinity at these points.)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b) Standard form for cot function: y=Acot(Bx-C), with period =&#960;/B, phase-shift=C/B, A=multiplier which stretches curve vertically.<BR>\n" );
document.write( "For given function, y=3 cot pi(x)/2, A=3, phase-shift=0<BR>\n" );
document.write( "period=&#960;/B=&#960;/(&#960;/2)=2<BR>\n" );
document.write( "Asymptotes: x=0 and x=2 (Note that at 0, and every period thereafter, tan x, the reciprocal of cot x, is approaching 0, so cot x is approaching infinity at these points.) </SPAN>\n" );
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