document.write( "Question 1187250: solve cos(3x) = cos(0.5x) for 0 <= x <= 180 degrees \n" ); document.write( "
Algebra.Com's Answer #818367 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"cos%283x%29\"\"%22%22=%22%22\"\"cos%280.5x%29\"\r\n" );
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document.write( "Write both angles in terms of their average.\r\n" );
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document.write( "Their average is \"%283x%2B0.5x%29%2F2\"\"%22%22=%22%22\"\"3.5x%2F2\"\"%22%22=%22%22\"\"1.75x\"\r\n" );
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document.write( "\"3x+=+1.75x%2B1.25x\" and \"0.5x+=+1.75x-1.25x\"\r\n" );
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document.write( "Substituting in original equation,\r\n" );
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document.write( "\"cos%281.75x%2B1.25x%29\"\"%22%22=%22%22\"\"cos%281.75x-1.25x%29\"\r\n" );
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document.write( "\"cos%281.75x%29cos%281.25x%29-sin%281.75x%29sin%281.25x%29%29\"\"%22%22=%22%22\"\"cos%281.75x%29cos%281.25x%29%2Bsin%281.75x%29sin%281.25x%29%29\"\r\n" );
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document.write( "\"cross%28cos%281.75x%29cos%281.25x%29%29-sin%281.75x%29sin%281.25x%29%29\"\"%22%22=%22%22\"\"cross%28cos%281.75x%29cos%281.25x%29%29%2Bsin%281.75x%29sin%281.25x%29%29\"\r\n" );
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document.write( "\"-2sin%281.75x%29sin%281.25x%29%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"sin%281.75x%29sin%281.25x%29%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"sin%281.75x%29\"\"%22%22=%22%22\"\"0\"; \"sin%281.25x%29%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"1.75x\"\"%22%22=%22%22\"\"180%5Eo%2An\";   \"1.25x\"\"%22%22=%22%22\"\"180%5Eo%2An\";\r\n" );
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document.write( "\"1.75=1%263%2F4=7%2F4\" and \"1.25=1%261%2F4=5%2F4\" so the above is\r\n" );
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document.write( "\"expr%287%2F4%29x\"\"%22%22=%22%22\"\"180%5Eo%2An\";   \"expr%285%2F4%29x\"\"%22%22=%22%22\"\"180%5Eo%2An\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"expr%284%2F7%29180%5Eo%2An\";   \"x\"\"%22%22=%22%22\"\"expr%284%2F5%29180%5Eo%2An\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28720%2F7%29%5Eo%2An\";   \"x\"\"%22%22=%22%22\"\"144%5Eo%2An\"\r\n" );
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document.write( "But since \"0+%3C=+x+%3C=+180%5Eo\",\r\n" );
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document.write( "\"0+%3C=+%28720%2F7%29%5Eo%2An+%3C=+180%5Eo\",    \"0+%3C=+144%5Eo%2An+%3C=+180%5Eo\", \r\n" );
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document.write( "\"0+%3C=+%28720%29%5Eo%2An+%3C=+1260%5Eo\",    \"0+%3C=+n+%3C=+180%5Eo%2F144%5Eo\", \r\n" );
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document.write( "\"0+%3C=+n+%3C=+1260%5Eo%2F720%5Eo\",    \"0+%3C=+n+%3C=+180%5Eo%2F144%5Eo\", \r\n" );
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document.write( "\"0+%3C=+n+%3C=+1.75\",    \"0+%3C=+n+%3C=+1.25\", \r\n" );
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document.write( "Since n is an integer, n is either 0 or 1.\r\n" );
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document.write( "So the solutions are\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28720%2F7%29%5Eo%2A0\";   \"x\"\"%22%22=%22%22\"\"144%5Eo%2A0\"\r\n" );
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document.write( "that is, x=0, and\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28720%2F7%29%5Eo%2A1\";   \"x\"\"%22%22=%22%22\"\"144%5Eo%2A1\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%28720%2F7%29%5Eo\";   \"x\"\"%22%22=%22%22\"\"144%5Eo\"\r\n" );
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document.write( "So there are 3 solutions.\r\n" );
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document.write( "\"x=0%5Eo\", \"x=%28720%2F7%29%5Eo\", and \"x=144%5Eo\"\r\n" );
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document.write( "Edwin

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