document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179523>Question 1179523</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can somebody please help me out with this??\r<BR>\n" );
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document.write( "Coastal areas experience tides which is where the ocean periodically gets to high and low points. Tides can be modeled with a sinusoidal (sine or cosine) function. At one beach, the high tide is 5 feet above mean sea level and the low tide is 5 feet below see level. The length of time between high and low tide is 6.5 hours. \r<BR>\n" );
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document.write( "If high tide is at time t=0 hours, give the function H(t) that describes the height of the tide relative to sea level t hours after the high tide.\r<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 #809074 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=809074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the basic form of the sine wave function is:<BR>\n" );
document.write( "y = a * sin(b * (x-c)) + d\r<BR>\n" );
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document.write( "a is the amplitude which, in this case, is 5 feet above the mean sea level and 5 feet below the mean seas level.<BR>\n" );
document.write( "the amplitude is therefore equal to 5.\r<BR>\n" );
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document.write( "b is the frequency.<BR>\n" );
document.write( "the frequency is equal to 360 degrees divided by the period.<BR>\n" );
document.write( "since the period is 6.5 hours, the frequency is equal to 360 / 13 which is equal to 27.69230769 rounded to 8 decimal places.\r<BR>\n" );
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document.write( "c is the horizontal displacement.<BR>\n" );
document.write( "this shifts the graph right or left.<BR>\n" );
document.write( "since you want the graph to shift 90 degrees to the left, then do the following.<BR>\n" );
document.write( "90/360 = 1/4 of a full cycle.<BR>\n" );
document.write( "when the full cycle is 13, then 1/4 of the full cycle is 13/4 = 3.25.<BR>\n" );
document.write( "if you want the shift to the left, then c must be negative which menns that, instead of x - c, you need x + c, because x - (-c) = x + c).<BR>\n" );
document.write( "the (x-c) part of the formula is therefore equal to x + 3.25).\r<BR>\n" );
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document.write( "d is the vertical displacement.<BR>\n" );
document.write( "this the value midpoint between the high and the low tides.\<BR>\n" );
document.write( "if d = 0, then the center line of the y value of the graph is y = 0.<BR>\n" );
document.write( "since this is where we want to be, then d = 0 and is therefore omitted because the default value of d is 0.\r<BR>\n" );
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document.write( "a word about default values.<BR>\n" );
document.write( "default value of a is 1.<BR>\n" );
document.write( "default value of c is 0<BR>\n" );
document.write( "default velus of b is 1<BR>\n" );
document.write( "default of value of d is 0.<BR>\n" );
document.write( "if all of these values are at default, then the equation becoms y = sin(x).<BR>\n" );
document.write( "that means a = 1, b = 1, c = 0 and d = 0.\r<BR>\n" );
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document.write( "your equation is y = 5 * sin(360/13) * (x + 3.25)<BR>\n" );
document.write( "the decimal version is y = 5 * sin(27.69230769 * (x + 3.25))\r<BR>\n" );
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document.write( "this is what the graph looks liike.\r<BR>\n" );
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document.write( "the graphing formula is y = 5 * sin(360/13 * (x + 3.25).\r<BR>\n" );
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document.write( "the h(t) formula is:\r<BR>\n" );
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document.write( "h(t) = 5 * sin(360/13 * (t + 3.25).\r<BR>\n" );
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document.write( "t is the amount of hours from t = 0.<BR>\n" );
document.write( "h(t) is the height of the tide at t hours from 0.\r<BR>\n" );
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document.write( "any questions, give me a shout.\r<BR>\n" );
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document.write( "theo </SPAN>\n" );
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