document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103234>Question 1103234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sinusoidal function has a maximum value of -5, a minimum value of -29, and <BR>\n" );
document.write( "consecutive minimum values when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-pi%2F5 ALIGN=MIDDLE  ALT=\"x=-pi%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+4pi%2F15 ALIGN=MIDDLE  ALT=\"x=+4pi%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Determine the phase shift </SPAN>\n" );
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document.write( "Note that \"sinusoidal\" can mean either a sine function or a cosine function. I will choose to use a sine function.<br><BR>\n" );
document.write( "The general form for the equation of a sine function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+A%2Asin%28B%28x-C%29%29%2BD ALIGN=MIDDLE  ALT=\"y+=+A%2Asin%28B%28x-C%29%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We are asked to find the phase shift, which is C.<br><BR>\n" );
document.write( "The function has consecutive minimum values at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-pi%2F5 ALIGN=MIDDLE  ALT=\"x=-pi%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+4pi%2F15 ALIGN=MIDDLE  ALT=\"x=+4pi%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The difference between those two values is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7pi%2F15 ALIGN=MIDDLE  ALT=\"7pi%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7pi%2F15 ALIGN=MIDDLE  ALT=\"7pi%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >; that means B is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F%287pi%2F15%29=30%2F7 ALIGN=MIDDLE  ALT=\"2pi%2F%287pi%2F15%29=30%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Since the given points are minimum values of the sine function, we want the phase shift to be 3/4 of the period (because sin(x) has its minimum value 3/4 of the way through a period), minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pi%2F5 ALIGN=MIDDLE  ALT=\"-pi%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=%283%2F4%29%287pi%2F15%29%2B%28pi%2F5%29+=+7pi%2F20%2B4pi%2F20+=+11pi%2F20 ALIGN=MIDDLE  ALT=\"C=%283%2F4%29%287pi%2F15%29%2B%28pi%2F5%29+=+7pi%2F20%2B4pi%2F20+=+11pi%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The phase shift is 11pi/20.<br><BR>\n" );
document.write( "The maximum and minimum values of the function are -5 and -29; in the formula, that makes A=12 and D=-17.<br><BR>\n" );
document.write( "So the complete function is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Asin%28%2830%2F7%29%28x%2B11pi%2F20%29%29-17 ALIGN=MIDDLE  ALT=\"12%2Asin%28%2830%2F7%29%28x%2B11pi%2F20%29%29-17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Here is a graph....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-pi%2Cpi%2C-35%2C5%2C12%2Asin%28%2830%2F7%29%28x%2B11pi%2F20%29%29-17%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-pi%2Cpi%2C-35%2C5%2C12%2Asin%28%2830%2F7%29%28x%2B11pi%2F20%29%29-17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The two minimum points closest to x=0 and on either of x=0 are at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-pi%2F5 ALIGN=MIDDLE  ALT=\"x=-pi%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+4pi%2F15 ALIGN=MIDDLE  ALT=\"x=+4pi%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );