document.write( "Question 451184: How do I develop the identity for \"sin%28expr%281%2F2%29a%29\" by using the identity for \"cos+%282a%29\"? \n" ); document.write( "
Algebra.Com's Answer #310294 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sin%28expr%281%2F2%29a%29\"\r\n" );
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document.write( "Start with the identity:\r\n" );
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document.write( "\"Cos%282alpha%29+=+Cos%5E2alpha+-+Sin%5E2alpha\"\r\n" );
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document.write( "\"Cos%282alpha%29+=+%281-Sin%5E2alpha%29+-+Sin%5E2alpha\"\r\n" );
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document.write( "\"Cos%282alpha%29+=+1-Sin%5E2alpha+-+Sin%5E2alpha\"\r\n" );
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document.write( "\"Cos%282alpha%29+=+1-2Sin%5E2alpha\" <-- sometimes this is given. If so you can start here\r\n" );
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document.write( "\"2Sin%5E2alpha+=+1+-+Cos%282alpha%29\"\r\n" );
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document.write( "\"Sin%5E2alpha+=+%281+-+Cos%282alpha%29%29%2F2\"\r\n" );
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document.write( "\"Sin%28alpha%29+=+%22%22+%2B-+sqrt%28%281+-+Cos%282alpha%29%29%2F2%29\"\r\n" );
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document.write( "Now substitute \"alpha=expr%281%2F2%29a\"\r\n" );
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document.write( "\"Sin%28expr%281%2F2%29a%29+=+%22%22+%2B-+sqrt%28%281+-+Cos%282expr%281%2F2%29a%29%29%2F2%29\"\r\n" );
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document.write( "Do one cancellation on the right:\r\n" );
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document.write( "\"Sin%28expr%281%2F2%29a%29+=+%22%22+%2B-+sqrt%28%281+-+Cos%28a%29%29%2F2%29\"\r\n" );
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document.write( "The sign to use depends on the quadrant\r\n" );
document.write( "in which the terminal side of \"expr%281%2F2%29a\" lies. \r\n" );
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document.write( "If the terminal side of \"expr%281%2F2%29a\" lies in the \r\n" );
document.write( "first or second quadrants, the identity uses the \r\n" );
document.write( "positive sign.\r\n" );
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document.write( "If the terminal side of \"expr%281%2F2%29a\" lies in the \r\n" );
document.write( "third or fourth quadrants, the identity uses the \r\n" );
document.write( "negative sign.\r\n" );
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document.write( "Edwin

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