document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140832>Question 1140832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the function y=3.5 sin(5x-80°)+1.5 by applying transformation to f(x) = sin x.<BR>\n" );
document.write( "State the amplitude, period, phase shift, and vertical shift. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761363 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=761363\">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=y=3.5sin%285x-80%29%2B1.5 ALIGN=MIDDLE  ALT=\"y=3.5sin%285x-80%29%2B1.5\"   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+-7%2C+7%2C+-7%2C+7%2C+3.5sin%285x-80%29%2B1.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-7%2C+7%2C+-7%2C+7%2C+3.5sin%285x-80%29%2B1.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "compare to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=Asin%28+Bx%2B-C+%29%2BD ALIGN=MIDDLE  ALT=\"y=Asin%28+Bx%2B-C+%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Amplitude: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+ ALIGN=MIDDLE  ALT=\"A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >(absolute value)\r<BR>\n" );
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document.write( "Period: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282pi%29%2FB+ ALIGN=MIDDLE  ALT=\"%282pi%29%2FB+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Phase Shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-C%2FB ALIGN=MIDDLE  ALT=\"-C%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Vertical Shift:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+D ALIGN=MIDDLE  ALT=\"+D\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "so, you have:\r<BR>\n" );
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document.write( "Amplitude: ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5 ALIGN=MIDDLE  ALT=\"3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Period: <BR>\n" );
document.write( "periodicity of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Asin%28bx%2B-c+%29 ALIGN=MIDDLE  ALT=\"a%2Asin%28bx%2B-c+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin_+base_+periodicity%29%2Fabs%28b%29 ALIGN=MIDDLE  ALT=\"%28sin_+base_+periodicity%29%2Fabs%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+ ALIGN=MIDDLE  ALT=\"sin%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >base periodicity is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=period=+360%2F5=+72 ALIGN=MIDDLE  ALT=\"period=+360%2F5=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
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document.write( "Vertical Shift: the graph shifts up by<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+D=1.5 ALIGN=MIDDLE  ALT=\"+D=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Phase Shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-C%2FB=80%2F5=16 ALIGN=MIDDLE  ALT=\"-C%2FB=80%2F5=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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