document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198042>Question 1198042</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the values of the constants, so that the function f(x)=acos[b(x-c)+d] models the  data (2.4,2.6) , (8.7,1.4), (14.7,2.6), (21,1.4), (27,2.6)\r<BR>\n" );
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document.write( "Possible answer one of the following:<BR>\n" );
document.write( "A) a=0.3 , b=1.8<BR>\n" );
document.write( "B) a=0.6 , c=2.4<BR>\n" );
document.write( "C) b=0.5 , c=3.4<BR>\n" );
document.write( "D) c=1.8 , d=4<BR>\n" );
document.write( "E) b=1.6 , d=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831750 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=831750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Since no one else has responded yet, I will provide mine....<br><BR>\n" );
document.write( "In my opinion, the problem is presented terribly; and it seems a terrible way to teach a student about sinusoidal functions.<br><BR>\n" );
document.write( "The problem asks us to find the values of the constants (a, b, c, and d) that make the general cosine function model the given data.<br><BR>\n" );
document.write( "Then the problem states \"Possible answer one of the following:\"<br><BR>\n" );
document.write( "That is not English; I suppose it means that one of the following A, B, C, D, or E is THE answer to the problem.  But none of those apparent answer choices gives the values of all four constants.<br><BR>\n" );
document.write( "So in order to work on the problem at all, we need to ignore the disconnect between the answer choices that each show 2 of the 4 constants and the instructions that say to find all 4 constants.<br><BR>\n" );
document.write( "Doing that, what can we determine from the given data points...?<br><BR>\n" );
document.write( "The given data points suggest that the period of the function is 12.3.  That is approximately equal to 4pi, which would make 0.5 a possible value for constant b.<br><BR>\n" );
document.write( "The given data points also suggest minimum and maximum values of 1.4 and 2.6, which would make d=2 and a=0.6 possible values for those constants.  But those values must also be approximate, because the two apparent minimum values of 1.4 are not at values of x that are exactly halfway between the successive apparent maximum values.<br><BR>\n" );
document.write( "And there appears to be nothing to say that 1.4 and 2.6 ARE the approximate minimum and maximum function values -- they might be intermediate values.<br><BR>\n" );
document.write( "That much discussion shows possible values for constants a, b, and d.  We can't say much about the possible values of constant c, because that depends on the value of constant b, and we only have a guess for a possible value for b.<br><BR>\n" );
document.write( "It appears to me that that is about all anyone can say about the problem........<br><BR>\n" );
document.write( " </SPAN>\n" );
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