document.write( "Question 41472: graph y=3sinx and y=sin 3x on the same axes. label the graph of each function.\r
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Algebra.Com's Answer #26761 by AnlytcPhil(1806) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "graph y=3sinx and y=sin 3x on the same axes. \r\n" );
document.write( "label the graph of each function.\r\n" );
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document.write( "I know the amp. of first function is 3 and\r\n" );
document.write( "period is 2p and for second function amp. is 1 \r\n" );
document.write( "and period is 2p/3 i just dont know how to graph\r\n" );
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document.write( "Draw the y-axis long enough to include both amplitudes \r\n" );
document.write( "as well as the opposite signs of the amplitudes:\r\n" );
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document.write( " 3|-\r\n" );
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document.write( " 2|-\r\n" );
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document.write( " 1|- \r\n" );
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document.write( " 0|-----------------------------------------------------------------------\r\n" );
document.write( "  |\r\n" );
document.write( "-1|-\r\n" );
document.write( "  |\r\n" );
document.write( "-2|-\r\n" );
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document.write( "-3|- \r\n" );
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document.write( "Divide the period of each by 4. \r\n" );
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document.write( "Dividing the first function's period by 4: 2p÷4 is p/2\r\n" );
document.write( "Multiply this by 0, 1, 2, 3, and 4\r\n" );
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document.write( "0p/2, 1p/2, 2p/2, 3p/2, 4p/2\r\n" );
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document.write( "or, reducing:\r\n" );
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document.write( "0, p/2, p, 3p/2, 2p\r\n" );
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document.write( "Positive sine functions go x-intercept, maximum, x-intercept, minimum,\r\n" );
document.write( "x-intercept. \r\n" );
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document.write( "Therefore it will have an x intercept at 0, a maximum at p/2, \r\n" );
document.write( "an x-intercept at p, a minimum at 3p/2 and an x-intercept at 2p\r\n" );
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document.write( "Dividing the second function's period by 4: (2p/3)÷4 is p/6\r\n" );
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document.write( "Multiply this by 0, 1, 2, 3, and 4\r\n" );
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document.write( "0p/6, 1p/6, 2p/6, 3p/6, 4p/6\r\n" );
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document.write( "or, reducing:\r\n" );
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document.write( "0, p/6, p, p/3, 2p/3\r\n" );
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document.write( "Positive sine functions go x-intercept, maximum, x-intercept, minimum,\r\n" );
document.write( "x-intercept. \r\n" );
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document.write( "Therefore it will have an x intercept at 0, a maximum at p/6, \r\n" );
document.write( "an x-intercept at p, a minimum at p/3 and an x-intercept at 2p/3\r\n" );
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document.write( "The LCD of periods p/6 and p/2 is 6, so mark off the x-axis in units of \r\n" );
document.write( "p/6, that is\r\n" );
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document.write( "1p/6, 2p/6, 3p/6, 4p/6, 5p/6, ... , 12p/6\r\n" );
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document.write( " 3|-\r\n" );
document.write( "  |\r\n" );
document.write( " 2|-\r\n" );
document.write( "  |\r\n" );
document.write( " 1|- \r\n" );
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document.write( "-0|----·----·----·----·----·----·----·----·----·----·----·----·------   \r\n" );
document.write( "  |  p/6  2p/6 3p/6 4p/6 5p/6 6p/6 7p/6 8p/6 9p/6 10p/6 11p/6 12p/6\r\n" );
document.write( "-1|-\r\n" );
document.write( "  |\r\n" );
document.write( "-2|-\r\n" );
document.write( "  |\r\n" );
document.write( "-3|-\r\n" );
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document.write( "I stopped at 12p/6 because that equals 2p, the larger period.\r\n" );
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document.write( "Reducing the ones of those that will reduce:\r\n" );
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document.write( "p/6, p/3, p/2, 2p/3, 5p/6, p, 7p/6, 4p/3, 3p/2, 5p/3, 11p/6, 2p.\r\n" );
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document.write( " 3|-\r\n" );
document.write( "  |\r\n" );
document.write( " 2|-\r\n" );
document.write( "  |\r\n" );
document.write( " 1|-\r\n" );
document.write( "  | \r\n" );
document.write( "-0|----·----·----·----·----·----·----·----·----·----·----·----·------   \r\n" );
document.write( "  |   p/6  p/3  p/2 2p/3 5p/6   p  7p/6 4p/3 3p/2 5p/3 11p/6 2p\r\n" );
document.write( "-1|-\r\n" );
document.write( "  |\r\n" );
document.write( "-2|-\r\n" );
document.write( "  |\r\n" );
document.write( "-3|-\r\n" );
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document.write( "Note that those values on the x-axis are about\r\n" );
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document.write( ".5, 1, 1.6, 2.1, 2.6, 3.14, 3.7, 4.2, 4.7, 5.2, 5.8, 6.28 \r\n" );
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document.write( "So the two graphs are\r\n" );
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document.write( "But you should extend the graph of y = sin(3x) to the\r\n" );
document.write( "length of the period of the graph of y = 3sin(x) like\r\n" );
document.write( "this:\r\n" );
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document.write( "You should also leave the x-axis markings in terms of p,\r\n" );
document.write( "rather than their numerical values as are on the graphs above. \r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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