document.write( "Question 1045173: Find all values of x in the interval [0, 2π] that satisfy the equation
\n" ); document.write( "6 cos(x) + 3 sin(2x) = 0 \n" ); document.write( "

Algebra.Com's Answer #660582 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "Find all values of x in the interval [0, 2π] that satisfy the equation
\n" ); document.write( "6 cos(x) + 3 sin(2x) = 0
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document.write( "6*cos(x) + 3*sin(2x) = 0,\r\n" );
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document.write( "Divide both sides by 3 and replace  sin(2x)  by  2*sin(x)*cos(x):  sin(2x) = 2*sin(x)*cos(x).  You will get\r\n" );
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document.write( "2*cos(x) + 2*sin(x)*cos(x) = 0.\r\n" );
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document.write( "Divide both sides by 2. You will get\r\n" );
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document.write( "cos(x) + sin(x)*cos(x) = 0.\r\n" );
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document.write( "Factorize: \r\n" );
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document.write( "cos(x)*(1+sin(x)) = 0.\r\n" );
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document.write( "The equation deploys in two independent equations:\r\n" );
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document.write( "1)  cos(x) = 0  --->  x =   and/or  x = .\r\n" );
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document.write( "2)  1+sin(x) = 0  --->  sin(x) = -1  --->  x = .\r\n" );
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document.write( "Answer. The solutions are   and .\r\n" );
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