document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117209>Question 1117209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of patriotic protesters near a wind turbine decide to place a flag on the tip of one blade. They notice that the flag is at its minimum height of 5 metres at t=6s and its maximum height of 17 metres at t=30s. \r<BR>\n" );
document.write( "\n" );
document.write( "Determine two equations of the sinusoidal function that describes the height of the flag in terms of time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732295 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13216)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=732295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "We are looking (I assume) for equations of the position as<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Asin%28b%28x-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"a%2Asin%28b%28x-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Acos%28b%28x-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"a%2Acos%28b%28x-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(1) The minimum and maximum values are 5 and 17. That means a is 6 and d is 11.<br><BR>\n" );
document.write( "(2) The minimum and maximum occur 24 seconds apart; that means the period is 48 seconds.  Then b is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282pi%29%2F48 ALIGN=MIDDLE  ALT=\"%282pi%29%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F24 ALIGN=MIDDLE  ALT=\"pi%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "(3a) For the sine function, the \"start\" of the period is when the value is 0 and increasing; that occurs at 18 seconds, so c is 18.<br><BR>\n" );
document.write( "(3b) For the cosine function, the \"start\" of the period is when the value is maximum; that occurs at 30 seconds, so c is 30.<br><BR>\n" );
document.write( "The two functions are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asin%28%28pi%2F24%29%28x-18%29%29%2B11 ALIGN=MIDDLE  ALT=\"6%2Asin%28%28pi%2F24%29%28x-18%29%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Acos%28%28pi%2F24%29%28x-30%29%29%2B11 ALIGN=MIDDLE  ALT=\"6%2Acos%28%28pi%2F24%29%28x-30%29%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Here are graphs of the two functions; the sine graph (red) is shifted up 1 unit and the cosine (green) graph down 1 unit so you can see the graphs of both functions.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-6%2C60%2C-4%2C20%2C6%2Asin%28%28pi%2F24%29%28x-18%29%29%2B12%2C6%2Acos%28%28pi%2F24%29%28x-30%29%29%2B10%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );