document.write( "Question 867653: sinē(1°)+sinē(2°)+···+sinē(88°)+sinē(89°) \n" ); document.write( "
Algebra.Com's Answer #523506 by Edwin McCravy(20064)\"\" \"About 
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document.write( "sinē(1°)+sinē(2°)+···+sinē(88°)+sinē(89°) =\r\n" );
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document.write( "Put some terms in the middle:\r\n" );
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document.write( "sinē(1°)+sinē(2°)+···+sinē(44°)+sinē(45°)+sinē(46°)+···+sinē(88°)+sinē(89°)\r\n" );
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document.write( "sinē(1°)+sinē(2°)+···+sinē(44°)+sinē(45°)+sinē(90°-44°)+···+sinē(90°-2°)+sinē(90°-1°)\r\n" );
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document.write( "Use the fact that sin(90°-q) = cos(q) \r\n" );
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document.write( "sinē(1°)+sinē(2°)+···+sinē(44°)+sinē(45°)+cosē(44°)+···+cosē(2°)+cosē(1°) =\r\n" );
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document.write( "Rearrange the terms putting the \r\n" );
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document.write( "1st and 89th terms together,\r\n" );
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document.write( "2nd and 88th terms together,\r\n" );
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document.write( "···\r\n" );
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document.write( "44th and 46th terms together: \r\n" );
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document.write( "[sinē(1°)+cosē(1°)]+[sinē(2°)+cosē(2°)]+···+[sinē(44°)+cosē(44°)]+sinē(45°) =\r\n" );
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document.write( "Use the fact that sinē(q)+cosē(q) = 1\r\n" );
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document.write( "1 + 1 + ··· + 1 + sinē(45°), where there are 44 1's.\r\n" );
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document.write( "44 + sinē(45°) =\r\n" );
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document.write( "44 + \"%28sqrt%282%29%2F2%29%5E2\" =\r\n" );
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document.write( "44 + \"2%2F4\" = \r\n" );
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document.write( "44 + \"1%2F2\" =\r\n" );
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document.write( "44.5 \r\n" );
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document.write( "Edwin

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