document.write( "Question 960361: if sin B=-1/5 with B in Quadrant 3, find cos B/2 \n" ); document.write( "
Algebra.Com's Answer #586901 by Edwin McCravy(20060) $\"\"$ $\"About$
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document.write( "Draw angle B in 3rd quadrant:\r\n" );
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document.write( "Since sine = , we make y=-1 and r=5, so that the sin(B)\r\n" );
document.write( "will be .\r\n" );
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document.write( "But we want cos(B) which is \r\n" );
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document.write( "Then we find x by the Pythagorean relation: \r\n" );
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document.write( "Since x goes to the left, we know to take the negative\r\n" );
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document.write( "So \r\n" );
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document.write( "Now use the formula\r\n" );
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document.write( "We need to determine whether to use the + or the - sign.\r\n" );
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document.write( "Since B is in the 3rd quadrant,  \r\n" );
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document.write( "Therefore  is in quadrant 2, and the cosine will be\r\n" );
document.write( "negative, so\r\n" );
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document.write( "Multiply numerator and denominator by 5 to simplify compound fraction:\r\n" );
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document.write( "That is the correct answer, but it has a square root within a square\r\n" );
document.write( "root, and often such an expression can be simplified to the sum or\r\n" );
document.write( "difference of two square roots of rational numbers.  Assume rational \r\n" );
document.write( "a and b exist so that\r\n" );
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document.write( "I will assume a difference since a difference occurs under the square\r\n" );
document.write( "root.\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "Multiply both sides by 10\r\n" );
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document.write( "We set rational parts equal and irrational parts equal\r\n" );
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document.write( ",  \r\n" );
document.write( ",     \r\n" );
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document.write( "Solve  for b, \r\n" );
document.write( "Substitute in \r\n" );
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document.write( " Multiply through by 25a\r\n" );
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document.write( ", \r\n" );
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document.write( "Using , substitute in\r\n" );
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document.write( "Using , substitute in\r\n" );
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document.write( "So we either have , or ,\r\n" );
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document.write( "But since  is negative we must choose\r\n" );
document.write( "the second answer:\r\n" );
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document.write( ",\r\n" );
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document.write( "So\r\n" );
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document.write( "Edwin
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