document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083859>Question 1083859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Anna rides a Ferris wheel at a county fair. At time t=0, Anna is at a height of 5 feet from the ground which is the minimum height of the Ferris wheel. The center of the Ferris Wheel is at a height of 85 feet. The Ferris Wheel rotates at a constant speed and makes two complete turns during the six minutes that Anna is on the Ferris Wheel.\r<BR>\n" );
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document.write( "Part A:<BR>\n" );
document.write( "Write a trigonometric function for h(t) to express Anna's height, in feet, in terms of time, t, in minutes. Explain how you determined you answer.\r<BR>\n" );
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document.write( "Part B:<BR>\n" );
document.write( "Determine Anna's height, in feet at time t= 1 minute  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697929 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697929\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general formula for a cosine function is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+A%2Acos%28+B%2At+%2B+C+%29+%2B+D+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+A%2Acos%28+B%2At+%2B+C+%29+%2B+D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28A%29+ ALIGN=MIDDLE  ALT=\"+abs%28A%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the amplitude <BR>\n" );
document.write( "<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;\" > is the phase shift<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+2%2Api+%29%2Fabs%28+B+%29+ ALIGN=MIDDLE  ALT=\"+%28+2%2Api+%29%2Fabs%28+B+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = period<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28+D+%29+ ALIGN=MIDDLE  ALT=\"+abs%28+D+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the vertical shift<BR>\n" );
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document.write( "(A)<BR>\n" );
document.write( "The plot of a point that is a minimum at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t=0+ ALIGN=MIDDLE  ALT=\"+t=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then goes to a maximum and back to a<BR>\n" );
document.write( "minimum would be a negative cosine function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-A%2Acos%28+B%2At+%2B+C+%29+%2B+D+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-A%2Acos%28+B%2At+%2B+C+%29+%2B+D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-80%2Acos%28+B%2At+%2B+C+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-80%2Acos%28+B%2At+%2B+C+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two turns in 6 minutes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+4%2Api+%29%2F6+=+%28+2%2Api+%29%2F3+ ALIGN=MIDDLE  ALT=\"+%28+4%2Api+%29%2F6+=+%28+2%2Api+%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B+=+%28+2%2Api+%29%2F3+ ALIGN=MIDDLE  ALT=\"+B+=+%28+2%2Api+%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+0+ ALIGN=MIDDLE  ALT=\"+C+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > since there will be no phase shift<BR>\n" );
document.write( "So now I have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( checking this, when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+6+ ALIGN=MIDDLE  ALT=\"+t+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B%2At+=+4%2Api+ ALIGN=MIDDLE  ALT=\"+B%2At+=+4%2Api+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is 2 turns )<BR>\n" );
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document.write( "(B)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1+ ALIGN=MIDDLE  ALT=\"+t+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%281%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281%29+=+-80%2Acos%28+.667%2Api+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%281%29+=+-80%2Acos%28+.667%2Api+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281%29+=+-80%2A%28-.5+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%281%29+=+-80%2A%28-.5+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281%29+=+40+%2B+85+=+125+ ALIGN=MIDDLE  ALT=\"+h%281%29+=+40+%2B+85+=+125+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At 1 min, her height is 125 ft<BR>\n" );
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document.write( "This kind of makes sense, because at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1.5+ ALIGN=MIDDLE  ALT=\"+t+=+1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "The ferris wheel is at maximum height:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281.5%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2A%283%2F2%29+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%281.5%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2A%283%2F2%29+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281.5%29+=+-80%2Acos%28+pi+%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%281.5%29+=+-80%2Acos%28+pi+%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281.5%29+=+-80%2A%28-1%29+%2B+85+ ALIGN=MIDDLE  ALT=\"+h%281.5%29+=+-80%2A%28-1%29+%2B+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281.5%29+=+165+ ALIGN=MIDDLE  ALT=\"+h%281.5%29+=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
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document.write( "Hope this helps -get other opinions if needed\r<BR>\n" );
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document.write( " </SPAN>\n" );
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