document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=923952>Question 923952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> T-table for graphing sine/cosine graph? I understand most of this image. I have to do this without a calculator that's why I have to set this up with a t-table. From the image I just need to know where to 4&#960;/4 comes from and why the phase shift goes from &#960;/2 to 2&#960;/4 I understand the rest it's just those two parts that make no sense to me. \r<BR>\n" );
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document.write( "http://i.imgur.com/R4sXLmZ.png \r<BR>\n" );
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document.write( "please help <BR>\n" );
document.write( "Thank you<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560506 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=560506\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sin%282x-pi%29 ALIGN=MIDDLE  ALT=\"y=sin%282x-pi%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=y+=+a+sin%28bx+%2B+c%29 ALIGN=MIDDLE  ALT=\"y+=+a+sin%28bx+%2B+c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> in your case  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-pi ALIGN=MIDDLE  ALT=\"c=-pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > in these graphs affect the phase shift (or displacement), given by:\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Phase_+shift=%28-c%29%2Fb ALIGN=MIDDLE  ALT=\"Phase_+shift=%28-c%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >  => in your case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-pi%29%2F2%29=pi%2F2 ALIGN=MIDDLE  ALT=\"%28-%28-pi%29%2F2%29=pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%29 ALIGN=MIDDLE  ALT=\"pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4pi%2F4%29 ALIGN=MIDDLE  ALT=\"4pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F2 ALIGN=MIDDLE  ALT=\"2pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and that was used because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > values\r<BR>\n" );
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document.write( "The choice of the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the table correspond  to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > intercepts, maxima  and minima points.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F4 ALIGN=MIDDLE  ALT=\"2pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0 ALIGN=MIDDLE  ALT=\"+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sin%282%282pi%2F4%29-4pi%2F4%29=sin%28pi-pi%29=sin%280%29=0 ALIGN=MIDDLE  ALT=\"y=sin%282%282pi%2F4%29-4pi%2F4%29=sin%28pi-pi%29=sin%280%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=3pi%2F4 ALIGN=MIDDLE  ALT=\"3pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sin%282%283pi%2F4%29-4pi%2F4%29=sin%283pi%2F2-2pi%2F2%29=sin%28pi%2F2%29=1 ALIGN=MIDDLE  ALT=\"y=sin%282%283pi%2F4%29-4pi%2F4%29=sin%283pi%2F2-2pi%2F2%29=sin%28pi%2F2%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=4pi%2F4 ALIGN=MIDDLE  ALT=\"4pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >| <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sin%282%284pi%2F4%29-4pi%2F4%29=sin%282pi-pi%29=sin%28pi%29=0 ALIGN=MIDDLE  ALT=\"y=sin%282%284pi%2F4%29-4pi%2F4%29=sin%282pi-pi%29=sin%28pi%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=5pi%2F4 ALIGN=MIDDLE  ALT=\"5pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sin%282%285pi%2F4%29-4pi%2F4%29=sin%285pi%2F2-2pi%2F2%29=sin%283pi%2F2%29=-1 ALIGN=MIDDLE  ALT=\"y=sin%282%285pi%2F4%29-4pi%2F4%29=sin%285pi%2F2-2pi%2F2%29=sin%283pi%2F2%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=6pi%2F4 ALIGN=MIDDLE  ALT=\"6pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sin%282%286pi%2F4%29-4pi%2F4%29=sin%283pi-pi%29=sin%282pi%29=0 ALIGN=MIDDLE  ALT=\"y=sin%282%286pi%2F4%29-4pi%2F4%29=sin%283pi-pi%29=sin%282pi%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=drawing%28+600%2C600%2C+-5%2C+5%2C+-5%2C+5%2Ccircle%28-pi%2C0%2C.1%29%2Clocate%28-3.2%2C-0.2%2C%28-pi%29%29%2Ccircle%28pi%2C0%2C.1%29%2Clocate%283%2C-0.3%2C%28pi%29%29%2Ccircle%28pi%2F2%2C0%2C.1%29%2Clocate%28pi%2F2%2C0%2C%28pi%2F2%29%29%2Ccircle%28-pi%2F2%2C0%2C.1%29%2Clocate%28-2%2C0%2C%28-pi%2F2%29%29%2C+graph%28+600%2C600%2C+-5%2C+5%2C+-5%2C+5%2C+sin%282x-pi%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "domain: all real numbers<BR>\n" );
document.write( "range:<BR>\n" );
document.write( "{ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3C=y%3C=1 ALIGN=MIDDLE  ALT=\"-1%3C=y%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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