document.write( "Question 711257: Find the exact value of cos1+cos2+cos3+.........+cos358+cos359 (use the concept of the unit cicle) no calculator.\r
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Algebra.Com's Answer #437355 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We use the fact that \r\n" );
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document.write( "cos(ϴ) = -cos(180°-ϴ) or cos(ϴ)+cos(180°-ϴ) = 0\r\n" );
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document.write( "cos(1°) + cos(179°) = 0\r\n" );
document.write( "cos(2°) + cos(178°) = 0\r\n" );
document.write( "cos(3°) + cos(177°) = 0\r\n" );
document.write( "...\r\n" );
document.write( "cos(87°) + cos(93°) = 0\r\n" );
document.write( "cos(88°) + cos(92°) = 0\r\n" );
document.write( "cos(89°) + cos(91°) = 0\r\n" );
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document.write( "cos(181°) + cos(359°)\r\n" );
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document.write( "and \r\n" );
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document.write( "We use the fact that\r\n" );
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document.write( "cos(180°+ϴ) = -cos(360°-ϴ) or cos(180°+ϴ)+cos(360°-ϴ) = 0\r\n" );
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document.write( "cos(181°) + cos(359°) = 0\r\n" );
document.write( "cos(182°) + cos(358°) = 0\r\n" );
document.write( "cos(183°) + cos(357°) = 0\r\n" );
document.write( "...\r\n" );
document.write( "cos(267°) + cos(273°) = 0\r\n" );
document.write( "cos(268°) + cos(272°) = 0\r\n" );
document.write( "cos(269°) + cos(271°) = 0\r\n" );
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document.write( "So all those cosines in the sum cancel out.\r\n" );
document.write( "Thus the only cosines in that sum that we haven't \r\n" );
document.write( "considered are \r\n" );
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document.write( "cos(90°) = 0, cos(180°) = -1, and cos(270°) = 0\r\n" );
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document.write( "And their sum is -1.   So that's the answer, -1.\r\n" );
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document.write( "Edwin
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