document.write( "Question 1093373: 3sinx+4cosx=5 \n" ); document.write( "

Algebra.Com's Answer #708003 by ikleyn(52879) $\"\"$ $\"About$

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document.write( "3sin(x) + 4cos(x) = 5  ---> \r\n" );
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document.write( " = 1.\r\n" );
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document.write( "Let \"a\" be the angle in QI such that cos(a) = ,  sin(a) = .\r\n" );
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document.write( "Such an angle does exists since  = 1.\r\n" );
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document.write( "Then \r\n" );
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document.write( "1 =  = cos(a)*sin(x) + sin(a)*cos(x) = sin(a+x) = sin(x+a).\r\n" );
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document.write( "It implies that x + a =  and, hence, x = ,  where a = \r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. x = $\"pi%2F2-arcsin%284%2F5%29\"$ .\r
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