document.write( "Question 1060384: Write 5sin(t)-12cos(t) in the form Asin(Bt+ϕ) using sum or difference formulas. \n" ); document.write( "
Algebra.Com's Answer #675350 by Edwin McCravy(20064)\"\" \"About 
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Write 5sin(t)-12cos(t) in the form Asin(Bt+ϕ) using sum or difference formulas.
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document.write( "We can just take B as 1.\r\n" );
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document.write( "\"5sin%28t%29-12cos%28t%29\"\"%22%22=%22%22\"\"A%2Asin%28t%2Bphi%29\"\"%22%22=%22%22\"\"A%2A%28sin%28t%29cos%28phi%29%5E%22%22%2Bcos%28t%29sin%28phi%29%5E%22%22%29\" \r\n" );
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document.write( "\"5sin%28t%29-12cos%28t%29\"\"%22%22=%22%22\"\"A%2A%28sin%28t%29cos%28phi%29%5E%22%22%2Bcos%28t%29sin%28phi%29%5E%22%22%29\"\r\n" );
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document.write( "\"5sin%28t%29-12cos%28t%29\"\"%22%22=%22%22\"\"A%2Asin%28t%29cos%28phi%29%5E%22%22%2BA%2Acos%28t%29sin%28phi%29%5E%22%22%29\"\r\n" );
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document.write( "So to make those identitically equal, we must have\r\n" );
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document.write( "(1)   \"A%2Acos%28phi%29\"\"%22%22=%22%22\"\"5\" and\r\n" );
document.write( "(2)   \"A%2Asin%28phi%29\"\"%22%22=%22%22\"\"-12\"\r\n" );
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document.write( "Dividing equals by equals, using (2) and (1)\r\n" );
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document.write( "   \"%28A%2Asin%28phi%29%29%2F%28A%2Acos%28phi%29%29\"\"%22%22=%22%22\"\"-12%2F5\"\r\n" );
document.write( "   \"%28sin%28phi%29%29%2F%28cos%28phi%29%29\"\"%22%22=%22%22\"\"-12%2F5\"\r\n" );
document.write( "   \"tan%28phi%29\"\"%22%22=%22%22\"\"-12%2F5\"\r\n" );
document.write( "   \"phi\"\"%22%22=%22%22\"\"%22-67.38013505%B0%22\"\r\n" );
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document.write( "To get a positive coterminal angle we add 360°\r\n" );
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document.write( "   \"phi\"\"%22%22=%22%22\"\"%22292.6198649%B0%22\"\r\n" );
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document.write( "   Squaring both sides of (1) and (2) and adding them:\r\n" );
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document.write( "\"A%5E2%2Acos%5E2%28phi%29%2BA%5E2%2Asin%5E2%28phi%29\"\"%22%22=%22%22\"\"5%5E2%2B%28-12%29%5E2\"\r\n" );
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document.write( "\"A%5E2%2A%28cos%5E2%28phi%29%2Bsin%5E2%28phi%29%29\"\"%22%22=%22%22\"\"25%2B144\"\r\n" );
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document.write( "\"A%5E2%2A%281%29\"\"%22%22=%22%22\"\"169\"\r\n" );
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document.write( "\"A%5E2\"\"%22%22=%22%22\"\"169\"\r\n" );
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document.write( "\"A\"\"%22%22=%22%22\"\"13\"\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "\"5sin%28t%29-12cos%28t%29\"\"%22%22=%22%22\"\"A%2Asin%28t%2Bphi%29\"\"%22%22=%22%22\"\"13sin%28t%2B%22292.6198649%B0%22%29\"\r\n" );
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document.write( "Edwin
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