document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=889034>Question 889034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) A Ferris wheel of a diameter 18.5 m rotates at a constant rate and makes a complete revolution in 10 seconds. If passengers board the lowest car at a height of 3 metres (m) above the ground, determine a Sine function that models the height, ( h ) in metres, of the car relative to the ground as a function of the time, (t) in seconds.  Hint: Draw a diagram to help you picture the Ferris wheel and think about what is happening through each of the given transformations! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537890 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=537890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "the function of the height of a circle from ground level in terms of degrees of angle where 0 degrees is the vertical line from the center of the circle to the ground is:\r<BR>\n" );
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document.write( "y = 9.25 - 9.25 * cos(x), where x is the number of degrees.\r<BR>\n" );
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document.write( "the graph of that function is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/072401.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "since the lowest car is 3 feet above the ground, this means that the center of the circle has to also be 3 feet above the ground, so you have to add 3 to this function to account for that.\r<BR>\n" );
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document.write( "the function then becomes:\r<BR>\n" );
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document.write( "y -9.25 - 9.25 * cos(x) + 3\r<BR>\n" );
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document.write( "the graph of that function is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/072402.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you want to graph the function in terms of time rather than degrees.\r<BR>\n" );
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document.write( "the ferris wheel rotates one revolution in 10 seconds.\r<BR>\n" );
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document.write( "this means the ferris wheeel rotates 1/10 of a revolution in 1 second.\r<BR>\n" );
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document.write( "one complete revolution is equal to 360 degrees, so the ferris wheel is rotating 1/10 of 360 = 36 degrees every second.\r<BR>\n" );
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document.write( "now you want to make x represent time rather than degrees, so the function becomes:\r<BR>\n" );
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document.write( "y = 9.25 - 9.25 * cos(36x) + 3\r<BR>\n" );
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document.write( "x now represents time in seconds rather than angle in degrees.<BR>\n" );
document.write( "after 1 second, the angle will be 36 degrees.<BR>\n" );
document.write( "after 2 seconds, the angle will be 72 degrees.<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "the graph of that function is shown below:\r<BR>\n" );
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document.write( "see below the graph for further comments.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/072403.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the first 2 graphs had their x-axis in terms of degrees starting from 0 degrees to 360 degrees.\r<BR>\n" );
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document.write( "the last graph had its x-axis in terms of seconds starting from 0 seconds to 10 seconds.\r<BR>\n" );
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document.write( "the function of y = 9.25 - 9.25 * cos(x) is where i started from.<BR>\n" );
document.write( "x repr3esented number of degrees at that time.\r<BR>\n" );
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document.write( "how i figured it out is as follows:\r<BR>\n" );
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document.write( "at 0 degrees, the height of the car is equal to 0 feet in height.<BR>\n" );
document.write( "this is before i added the 3 feet to adjust for the fact that at 0 degrees the car was actually 3 feet in height.\r<BR>\n" );
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document.write( "at 90 degrees, the height of the car is equal to 9.25 feet.\r<BR>\n" );
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document.write( "at 180 degrees, the height of the car is equal to 18.5 feet.\r<BR>\n" );
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document.write( "at 270 degrees, the height of the car is equal to 9.25 feet.\r<BR>\n" );
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document.write( "at 360 degrees, the height of the car is back to 0 feet again.\r<BR>\n" );
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document.write( "the following diagram shows that relationship.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/072404.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the following diagram shows how the height of he ferris wheel was calculated.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/072405.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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