document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202354>Question 1202354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f is such that f(x) = a - bcosx for 0° ≤ x ≤ 360°, where a and b are positive constants. The maximum value of f(x) is 10 and the minimum value is -2.<BR>\n" );
document.write( "i) Find the values of a and b,<BR>\n" );
document.write( "ii) Solve the equation f(x)=0,<BR>\n" );
document.write( "iii)Sketch the graph of y=f(x)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837117 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837117\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (i)\r<BR>\n" );
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document.write( "The max and min are 10 and -2 respectively.<BR>\n" );
document.write( "The midpoint of the max and min is (10+(-2))/2 = (10-2)/2 = 8/2 = 4, which is the value of 'a'. <BR>\n" );
document.write( "This is the midline. \r<BR>\n" );
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document.write( "The function updates to f(x) = 4 - b*cos(x)\r<BR>\n" );
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document.write( "Cosine maxes out when x = 0 degrees. <BR>\n" );
document.write( "Cos(x) = cos(0) = 1<BR>\n" );
document.write( "When cosine is maxed out, 4 - b*cos(x) will reach its minimum. In this case, the min is -2\r<BR>\n" );
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document.write( "4 - b*cos(x) = -2<BR>\n" );
document.write( "4 - b*cos(0) = -2<BR>\n" );
document.write( "-b*1 = -2-4<BR>\n" );
document.write( "-b  = -6<BR>\n" );
document.write( "b = 6\r<BR>\n" );
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document.write( "Therefore, the function is f(x) = 4 - 6*cos(x)\r<BR>\n" );
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document.write( "Answers: <font color=red>a = 4, b = 6</font>\r<BR>\n" );
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document.write( "Part (ii)\r<BR>\n" );
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document.write( "f(x) = 4 - 6*cos(x)<BR>\n" );
document.write( "0 = 4 - 6*cos(x)<BR>\n" );
document.write( "6cos(x) = 4<BR>\n" );
document.write( "cos(x) = 4/6<BR>\n" );
document.write( "x = arccos(4/6) or x = -arccos(4/6)<BR>\n" );
document.write( "x = 48.189685 or x = -48.189685 approximately\r<BR>\n" );
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document.write( "The angle -48.189685 is not in the interval 0° ≤ x ≤ 360°, but adding 360 to it will find a coterminal angle.<BR>\n" );
document.write( "-48.189685 + 360 = 311.810315\r<BR>\n" );
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document.write( "Answers: <font color=red>x = 48.189685, x = 311.810315</font> (both are approximate)\r<BR>\n" );
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document.write( "Part (iii)\r<BR>\n" );
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document.write( "I recommend graphing apps such as Desmos and GeoGebra.\r<BR>\n" );
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document.write( "Here's the link to the interactive Desmos graph.<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.desmos.com/calculator/roduixexnc\">https://www.desmos.com/calculator/roduixexnc</a><BR>\n" );
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