document.write( "Question 1090465: sin(x+y)=sin(x)cos(y)+sin(y)cos(x)
\n" ); document.write( "20 sin(x)+21 cos(x). \n" ); document.write( "
Algebra.Com's Answer #704906 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"20sin%28x%29%2B21cos%28x%29\"\r\n" );
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document.write( "We draw a right triangle with legs having the lengths of those\r\n" );
document.write( "two coefficients.  We put the 20 on the adjacent side to y\r\n" );
document.write( "and 21 on the opposite side, so that we can use the given \r\n" );
document.write( "sin(x+y) formula.  [If we did it the other way we'd have to \r\n" );
document.write( "use the cos(x-y) formula.]\r\n" );
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document.write( "Note here that y is the angle whose tangent is 21/20, and we\r\n" );
document.write( "state that mathematically by the equation y = tan-1(21/20).\r\n" );
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document.write( "We calculate the hypotenuse by the Pythagorean theorem:\r\n" );
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document.write( "\"c%5E2=a%5E2%2Bb%5E2\"\r\n" );
document.write( "\"c%5E2%2B20%5E2%2B21%5E2\"\r\n" );
document.write( "\"c%5E2=400%2B441\"\r\n" );
document.write( "\"c%5E2=841\"\r\n" );
document.write( "\"c=sqrt%28841%29\"\r\n" );
document.write( "\"c=29\"\r\n" );
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document.write( "We multiply the given expression, which is \r\n" );
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document.write( "\"20sin%28x%29%2B21cos%28x%29\"\r\n" );
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document.write( "by \"29%2A%281%2F29%29\" which is the same as multiplying\r\n" );
document.write( "by 1, and does not change the value:\r\n" );
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document.write( "\"29%281%2F29%29%2820sin%28x%29%5E%22%22%2B21cos%28x%29%29\"\r\n" );
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document.write( "We distribute the \"%281%2F29%29\"\r\n" );
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document.write( "\"29%28expr%2820%2F29%29sin%28x%29%2Bexpr%2821%2F29%29cos%28x%29%29\"\r\n" );
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document.write( "We use the right triangle above to substitute trig\r\n" );
document.write( "ratios for the fractions:\r\n" );
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document.write( "\"29%28cos%28y%29%5E%22%22sin%28x%29%2Bsin%28y%29cos%28x%29%29\"\r\n" );
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document.write( "We rearrange the factors in the parentheses so that \r\n" );
document.write( "what's inside the parentheses will look like the right \r\n" );
document.write( "side of the given formula sin(x+y)=sin(x)cos(y)+sin(y)cos(x)\r\n" );
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document.write( "\"29%28sin%28x%29%5E%22%22cos%28y%29%2Bsin%28y%29cos%28x%29%29\"\r\n" );
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document.write( "We replace the parentheses using the given formula:\r\n" );
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document.write( "\"29sin%28x%2By%29\", where y = tan-1(21/20).\r\n" );
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document.write( "Edwin
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