document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134825>Question 1134825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete the chart and find equations describing the trig function:\r<BR>\n" );
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document.write( "X values: 4, 4.9, 5.8, 6.7, 7.6<BR>\n" );
document.write( "Y values: 13, 4.5, -4, 4.5, 13\r<BR>\n" );
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document.write( "A: <BR>\n" );
document.write( "B:<BR>\n" );
document.write( "C:<BR>\n" );
document.write( "D:\r<BR>\n" );
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document.write( "Write in form y=d+acos(b(x-c)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752514 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=752514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The function has a maximum value of 13 at x=4 and again at x=7.6, so the period is 7.6-4 = 3.6.<br><BR>\n" );
document.write( "The function has a minimum value of -4 halfway through the period, at x=5.8.  So the oscillation is between -4 and 13; that makes the amplitude 8.5 and the centerline 4.5.<br><BR>\n" );
document.write( "The basic cosine graph has its maximum at 0; since this function has its \"first\" maximum at x=4, the phase shift is 4.<br><BR>\n" );
document.write( "In the equation<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%2Acos%28b%28x-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"y+=+a%2Acos%28b%28x-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a is the amplitude, c is the phase shift, and d is the vertical shift.<br><BR>\n" );
document.write( "At this point we know a=8.5, c=4, and d=4.5; we need to determine b, which determines the period.<br><BR>\n" );
document.write( "The value of b, to get the length of the period equal to 3.6, is<br><BR>\n" );
document.write( "b = (2pi)/3.6<br><BR>\n" );
document.write( "So the complete function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8.5%2Acos%28%282pi%2F3.6%29%28x-4%29%29%2B4.5 ALIGN=MIDDLE  ALT=\"y+=+8.5%2Acos%28%282pi%2F3.6%29%28x-4%29%29%2B4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Here is a graph, with horizontal lines showing the maximum and minimum values and the centerline of the function.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C10%2C-6%2C16%2C8.5%2Acos%28%282pi%2F3.6%29%28x-4%29%29%2B4.5%2C13%2C-4%2C4.5%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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