document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140827>Question 1140827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is my question. <BR>\n" );
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document.write( "And this is what I have so far. I just need help putting all this information into the equation. I don't understand that.<BR>\n" );
document.write( "a is the amplitude;<BR>\n" );
document.write( "the period is 360/b (assuming x is in degrees);<BR>\n" );
document.write( "the horizontal shift is c (0 in this example);<BR>\n" );
document.write( "d is the vertical shift (axis, or center line)\r<BR>\n" );
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document.write( "The center line is halfway between the minimum and maximum values; in this example the minimum and maximum values are 0 and 4. That gives you the value of d.\r<BR>\n" );
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document.write( "The amplitude a is half the difference between the minimum and maximum values.\r<BR>\n" );
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document.write( "because we are using a sine function the horizontal shift is 0.\r<BR>\n" );
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document.write( "The period is 180 degrees; that gives you the value of b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761376 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=761376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i got it, but it wasn't easy.\r<BR>\n" );
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document.write( "i had to play around with the graph to understand what was going on.\r<BR>\n" );
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document.write( "the easier parts are as follows.\r<BR>\n" );
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document.write( "the highest value is 4 and the lowest value is 0.\r<BR>\n" );
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document.write( "that makes the amplitude 4 / 2 = 2.\r<BR>\n" );
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document.write( "that makes the vertical displacement equal to 2 because the center line has to be halfway between the high point and the low points.\r<BR>\n" );
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document.write( "the graph looks like it can be modeled with a cosine function, so that's what i used.\r<BR>\n" );
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document.write( "so far i have y = 2 * cosine (x) + 2.\r<BR>\n" );
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document.write( "the period is 180 degrees, so the frequency has to be 360 / 180 = 2.\r<BR>\n" );
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document.write( "that makes the equation y = 2 * cosine (2 * x) + 2.\r<BR>\n" );
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document.write( "the graph of that equation is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/051021.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( "what's left is the horizontal shift.\r<BR>\n" );
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document.write( "at first i found it the easy way.\r<BR>\n" );
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document.write( "that was to create a horizontal line at y = 2.5 and then find that value of x on the graph gave me that.\r<BR>\n" );
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document.write( "it turned out that the value of y = 2.5 was at x = -37.761 degrees.\r<BR>\n" );
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document.write( "that graph is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/051022.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "to make that value of y = 2.5 show up when x = 0, i needed to shift the graph to the right 37.761 degrees.\r<BR>\n" );
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document.write( "the equation became y = 2 * cos(2 * (x - 37.761)) + 2.\r<BR>\n" );
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document.write( "that graph is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/051023.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the graph now looks like what your diagram shoed you, even though that diagram was not that easy to figure out.\r<BR>\n" );
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document.write( "the hard way to figure out what to do for the horizontal displacement was as follows.\r<BR>\n" );
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document.write( "since the cosine function was displaced 2 unit vertically up, i figured that the value of the cosine function needed to be .5 when x = 0.\r<BR>\n" );
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document.write( "i used my calculator to find that the angle was 60 degrees because arc cosine (.5) = 60 degrees.\r<BR>\n" );
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document.write( "however, since the amplitude was 2, in order to get a cosine value of .5, i needed to get a cosine value of .25 because 2 * .25 = .5.\r<BR>\n" );
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document.write( "therefore i looked for the angle that had a cosine value of .25.\r<BR>\n" );
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document.write( "that angle was 75.52248781.\r<BR>\n" );
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document.write( "since it occured before x = 0, the angle was actually -75.52248781 degrees.\r<BR>\n" );
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document.write( "but, since the frequency was 2, i needed to get half of that angle which made it -37.76124391.\r<BR>\n" );
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document.write( "that's the angle i found by looking at the graph, only it was rounded to 3 decimal digits.\r<BR>\n" );
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document.write( "that was close enough for graphing purposes, so i got what i wanted without having to put in the full angle, i.e. the rounded angle to 3 decimal digits was good enough.\r<BR>\n" );
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document.write( "doing it from the graph as i initially did was much easier.\r<BR>\n" );
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document.write( "doing it from the equation and using some logic was much harder.\r<BR>\n" );
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document.write( "i did arrive at the same solution, however, which is good.\r<BR>\n" );
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document.write( "any questions, write to dtheophilis@gmail.com.\r<BR>\n" );
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document.write( "you were asked to determine the equation.\r<BR>\n" );
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document.write( "the equation is y = 2 * cosine (2 * (x - 37.76124391)) + 2\r<BR>\n" );
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