document.write( "Question 1160906: For the following table of data, determine an equation of a sine function that satisfies the given data.\r
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Algebra.Com's Answer #785110 by Edwin McCravy(20062) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "x  | -120° | -60° |  0°  | 60° | 120° | 180° | 240° |\r\n" );
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document.write( "y  |   1.5 |   3  | 1.5  |  0  | 1.5  |  3   | 1.5  |    \r\n" );
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document.write( "This is the graph:\r\n" );
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document.write( "The equation is\r\n" );
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document.write( "where  |A| = amplitude = (maximum value - minimum value)/2 = (3-0)/2 = 3/2,\r\n" );
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document.write( "So we substitute 3/2 for A\r\n" );
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document.write( "The period = 360°/B = length of one cycle. The first cycle goes from\r\n" );
document.write( "-120° to 120° which is 120°-(-120°) = 120°+120° = 240°\r\n" );
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document.write( "So 360°/B = 240°\r\n" );
document.write( "     360° = 240°B\r\n" );
document.write( "360°/240° = B\r\n" );
document.write( "      3/2 = B\r\n" );
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document.write( "We substitute 3/2 for B:\r\n" );
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document.write( "The phase (horizontal) shift, as we can tell from the graph, is 120° LEFT,\r\n" );
document.write( "so C/B is +120°. (+ if left, and - if right)\r\n" );
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document.write( "C/B = 120°\r\n" );
document.write( "  C = 120°B\r\n" );
document.write( "  C = 120°(3/2)\r\n" );
document.write( "  C = 180°\r\n" );
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document.write( "We substitute 180° for C\r\n" );
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document.write( "Finally the vertical shift is D and we can see that the graph has a\r\n" );
document.write( "vertical shift upward of 1.5, so we substitute 1.5 for D:\r\n" );
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document.write( "And since 1.5 = 3/2 we can just write 3/2 for 1.5 and all the\r\n" );
document.write( "constants just happened to came out to be 3/2.\r\n" );
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document.write( "Edwin

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