document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159753>Question 1159753</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In comparison to the graph y=3cosx, specifically describe the type of transformation of the graph of y=3cos(x+Pi/3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782823 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=782823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In comparison to the graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3cos%28x%29 ALIGN=MIDDLE  ALT=\"y=3cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, specifically describe the type of transformation of the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3cos%28x%2Bpi%2F3%29 ALIGN=MIDDLE  ALT=\"y=3cos%28x%2Bpi%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let us first look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3cos%28x%29 ALIGN=MIDDLE  ALT=\"y=3cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " compare it  to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+A+cos+%28Bx+%2B+C%29+ ALIGN=MIDDLE  ALT=\"y+=+A+cos+%28Bx+%2B+C%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=A+=+3 ALIGN=MIDDLE  ALT=\"A+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >... amplitude<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+1 ALIGN=MIDDLE  ALT=\"B+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........If B is equal to 1, then it takes 2pi to complete a period; so, a period is 2pi<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+0 ALIGN=MIDDLE  ALT=\"C+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........no horizontal displacement (or shift)\r<BR>\n" );
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document.write( "It is easy to characterize the effect of changes in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" >  as a mapping  (<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;\" >)  to (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+C ALIGN=MIDDLE  ALT=\"x+%2B+C\"   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;\" >) and this is a translation either moving the graph to the left if C is positive, or to the right if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative.\r<BR>\n" );
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document.write( "now look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3cos%28x%2Bpi%2F3%29 ALIGN=MIDDLE  ALT=\"y=3cos%28x%2Bpi%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  compare it  to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3cos%28x%29 ALIGN=MIDDLE  ALT=\"y=3cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "only difference is the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+ ALIGN=MIDDLE  ALT=\"C+\"   DISABLED_style= \"max-width:90%; height:auto;\" >which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3 ALIGN=MIDDLE  ALT=\"pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%3E0+ ALIGN=MIDDLE  ALT=\"C%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " and this is a translation moving the graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3 ALIGN=MIDDLE  ALT=\"pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=left+ ALIGN=MIDDLE  ALT=\"left+\"   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%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0Alocate%281%2C2%2Chighlight%28y=3cos%28x%29%29%29%2Clocate%281%2C-2%2Chighlight%28green%28y=3cos%28x%2Bpi%2F3%29%29%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+3cos%28x%29%2C+3cos%28x%2Bpi%2F3%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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