document.write( "Question 1044552: Good evening, I need help to understand step by step this equation:
\n" ); document.write( "sin(4x + 20°) + sin(2x + 10°) = 0
\n" ); document.write( "My first solution is: x = -5° +k.60° and that is correct
\n" ); document.write( "The second solution should be: x = 85° +k.180° but I cannot reach it
\n" ); document.write( "Can somebody explain me how to solve? Thank you very much RB \n" ); document.write( "

Algebra.Com's Answer #659874 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "Good evening, I need help to understand step by step this equation:
\n" ); document.write( "sin(4x + 20°) + sin(2x + 10°) = 0
\n" ); document.write( "My first solution is: x = -5° +k.60° and that is correct
\n" ); document.write( "The second solution should be: x = 85° +k.180° but I cannot reach it
\n" ); document.write( "Can somebody explain me how to solve? Thank you very much RB
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document.write( "Notice that  4x + 20° = 2*(2x + 10°).\r\n" );
document.write( "So you actually have an equation\r\n" );
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document.write( " = \r\n" );
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document.write( "with  = 2x + 10°.\r\n" );
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document.write( "Next, as you probably know,   = 2*sin(alpha)*cos(alpha), and, therefore, your equation takes the form\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " = .\r\n" );
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document.write( "It deploys in two independent equations\r\n" );
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document.write( "1.  sin(2x+10°) = 0  --->  2x+10° = 90° or 2x+10° = 180° or 2x+10° = 360° or 2x+10° = 540° --->  \r\n" );
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document.write( "    x = 40°  or  x = 85°  or  x = 175°  or  x = 265°.\r\n" );
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document.write( "2.  cos(2x+10°) =   --->  2x+10° = 120° or 2x+10° = 240° or 2x+10° = 480°  or 2x+10° = 600° --->\r\n" );
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document.write( "    x = 55°  or  x = 115°  or  x = 235°  or  x = 285°.\r\n" );
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document.write( "Answer.  x = 40° or x = 85° or x = 175° or x = 265° or\r\n" );
document.write( "         x = 55° or x = 115° or x = 235° or x = 285°.\r\n" );
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