document.write( "Question 814362: Use a half-angle identity to find the exact value of this expression. \r
\n" ); document.write( "\n" ); document.write( "Given sin $\"%28theta%29\"$ = $\"2sqrt%282%29%2F3\"$ , 0° < $\"theta\"$ < 90°,\r
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Algebra.Com's Answer #490284 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Use a half-angle identity to find the exact value of this expression. \r\n" );
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document.write( "Given sin = , 0° <  < 90°,\r\n" );
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document.write( "find cos \r\n" );
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document.write( "We are given sin = \r\n" );
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document.write( "cos = \r\n" );
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document.write( " is a positive number, the sine is positive in the first two\r\n" );
document.write( " quadrants so 0° <  < 180° and 0° <  < 90°,\r\n" );
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document.write( "so we take the positive and cos = \r\n" );
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document.write( "So everything's positive and in the first quadrant.\r\n" );
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document.write( "Since sin =  and the sine is the opposite over the hypotenuse,\r\n" );
document.write( "we draw a right triangle containing  with the length of the opposite side as\r\n" );
document.write( "the numerator of  and the hypotenuse as the denominator of . \r\n" );
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document.write( "Before drawing the right triangle, we calculate the adjacent side using the\r\n" );
document.write( "Pythagorean theorem:\r\n" );
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document.write( "c² = a² + b²\r\n" );
document.write( "3² = a² + \r\n" );
document.write( " 9 = a² + 4·2\r\n" );
document.write( " 9 = a² + 8\r\n" );
document.write( " 1 = a²\r\n" );
document.write( " 1 = a \r\n" );
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document.write( "So the right triangle is like this: \r\n" );
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document.write( "cos = \r\n" );
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document.write( "From the right triangle, we can get cos by\r\n" );
document.write( "using the fact that the cosine is the adjacent over the \r\n" );
document.write( "hypotenuse .  Substituting:\r\n" );
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document.write( "cos = \r\n" );
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document.write( "To simplify the compound fraction under the radical we multiply\r\n" );
document.write( "top and bottom by 3\r\n" );
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document.write( "cos = \r\n" );
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document.write( "cos = \r\n" );
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document.write( "cos = \r\n" );
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document.write( "cos = \r\n" );
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document.write( "Rationalize the denominator by multiplying top and bottom by 3\r\n" );
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document.write( "cos = \r\n" );
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document.write( "cos = \r\n" );
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document.write( "cos = \r\n" );
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document.write( "Edwin

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