document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=859627>Question 859627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My Algebra II teacher has assigned me a long worksheet that has to do with a Ferris wheel. And I need to \"Identify the amplitude, the period, the phase shift, and the center line for my curve. Write the equation of my sinusoid curve [I have never heard that word before] in terms of (i) the sine functions and (ii) the cosine function.\" So basically I believe I just need to find the equations. I have the data below:\r<BR>\n" );
document.write( "\n" );
document.write( " X=time in seconds      /                Y=height in meters<BR>\n" );
document.write( "0                       /                 5.5<BR>\n" );
document.write( "10                      /                 10<BR>\n" );
document.write( "20                      /                 14.5<BR>\n" );
document.write( "30                      /                 18<BR>\n" );
document.write( "40                      /                 19.5<BR>\n" );
document.write( "50                      /                 18<BR>\n" );
document.write( "60                      /                 14.5<BR>\n" );
document.write( "70                      /                 10<BR>\n" );
document.write( "80                      /                 5.5<BR>\n" );
document.write( "90                      /                 2.5<BR>\n" );
document.write( "100                     /                 1.5<BR>\n" );
document.write( "110                     /                 2.5\r<BR>\n" );
document.write( "\n" );
document.write( "Any help is beneficial for me, thank you so much for your time </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517874 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=517874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> My Algebra II teacher has assigned me a long worksheet that has to do with a Ferris wheel. And I need to \"Identify the amplitude, the period, the phase shift, and the center line for my curve. Write the equation of my sinusoid curve [I have never heard that word before] in terms of (i) the sine functions and (ii) the cosine function.\" So basically I believe I just need to find the equations. I have the data below:\r<BR>\n" );
document.write( "\n" );
document.write( " X=time in seconds      /                Y=height in meters<BR>\n" );
document.write( "0                       /                 5.5<BR>\n" );
document.write( "10                      /                 10<BR>\n" );
document.write( "20                      /                 14.5<BR>\n" );
document.write( "30                      /                 18<BR>\n" );
document.write( "40                      /                 19.5<BR>\n" );
document.write( "50                      /                 18<BR>\n" );
document.write( "60                      /                 14.5<BR>\n" );
document.write( "70                      /                 10<BR>\n" );
document.write( "80                      /                 5.5<BR>\n" );
document.write( "90                      /                 2.5<BR>\n" );
document.write( "100                     /                 1.5<BR>\n" );
document.write( "110                     /                 2.5<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Look for the max and min heights.<BR>\n" );
document.write( "40                      /                 19.5 is the max<BR>\n" );
document.write( "100                     /                 1.5 is the min<BR>\n" );
document.write( "It makes 1/2 of a revolution in 60 seconds --> period = 120 seconds/revolution<BR>\n" );
document.write( "Amplitude is 1/2 of the difference, (19.5 - 1.5)/2 = 9 meters<BR>\n" );
document.write( "The axis of the wheel is (min + max)/2 = 10.5 meters AGL<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "A sine function is<BR>\n" );
document.write( "f(t) = Asin(t)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y = f(x) = 9*sin(2pi*x/120) --> Amp of 9, and period of 120 seconds<BR>\n" );
document.write( "Add 10.5<BR>\n" );
document.write( "y = 9*sin(pi*x/60) + 10.5<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "The sine of 0 is 0, tho, so it needs a phase shift to make it 5.5 at x=0.<BR>\n" );
document.write( "9*sin((2pi*(x - 11.20415))/120) + 10.5 fits.  Finding the phase shift required some interpolation.<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "9*sin((2pi*(x - 11.20415))/120) + 10.5<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "9*cos(90 - (2pi*x - 11.20415)/120) + 10.5 </SPAN>\n" );
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