document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202328>Question 1202328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sinusoidal function has an amplitude of 8 units, ad period of 180, and a minimum at (0, -3). Determine the equation of the function.<BR>\n" );
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document.write( "Answer: <font color=red size=4>y = -8cos(2x)+5</font><BR>\n" );
document.write( "This is when we are in degree mode.<BR>\n" );
document.write( "Other answers are possible.\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "The template for cosine is<BR>\n" );
document.write( "y = A*cos(B(x-C))+D\r<BR>\n" );
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document.write( "where,<BR>\n" );
document.write( "|A| = amplitude<BR>\n" );
document.write( "B = used to find the period<BR>\n" );
document.write( "C = phase shift<BR>\n" );
document.write( "D = midline\r<BR>\n" );
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document.write( "|A| = 8 leads to either A = 8 or A = -8<BR>\n" );
document.write( "Let's go with A = -8 because A = 8 will make x = 0 lead to a max, when we want x = 0 to lead to a min instead.\r<BR>\n" );
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document.write( "\"period of 180\" seems to imply your teacher wants things in degree mode (rather than radians).<BR>\n" );
document.write( "T = 180 = period<BR>\n" );
document.write( "B = 360/T<BR>\n" );
document.write( "B = 360/180<BR>\n" );
document.write( "B = 2\r<BR>\n" );
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document.write( "To make things simple, I'll have the phase shift be set to C = 0.\r<BR>\n" );
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document.write( "One minimum point is located at (0,-3)<BR>\n" );
document.write( "The smallest y output possible is y = -3<BR>\n" );
document.write( "Go up 8 units, the amplitude amount, to arrive at y = -3+8 = 5 which is the midline<BR>\n" );
document.write( "Therefore, D = 5\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "A = -8<BR>\n" );
document.write( "B = 2<BR>\n" );
document.write( "C = 0<BR>\n" );
document.write( "D = 5\r<BR>\n" );
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document.write( "y = A*cos(B(x-C))+D<BR>\n" );
document.write( "y = -8*cos(2(x-0))+5<BR>\n" );
document.write( "<font color=red>y = -8cos(2x)+5</font>\r<BR>\n" );
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document.write( "Graph<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.desmos.com/calculator/gigkk7becm\">https://www.desmos.com/calculator/gigkk7becm</a><BR>\n" );
document.write( "GeoGebra is another graphing option I recommend. </SPAN>\n" );
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