document.write( "Question 1070334: Please help me solve this question\r
\n" ); document.write( "\n" ); document.write( "If A=340 degree then 2sinA/2 is identical to
\n" ); document.write( "A) √(1+sinA) + √(1-sinA)
\n" ); document.write( "B)-√(1+sinA) - √(1-sinA)
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Algebra.Com's Answer #685452 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The answer can be found immediately with a calculator.  However\r\n" );
document.write( "since you are asking this, I am supposing you are asking to show \r\n" );
document.write( "why without using any numerical calculations.  You can use only \r\n" );
document.write( "information about the signs in the various quadrants and the fact\r\n" );
document.write( "that an angle is increasing in QI\r\n" );
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document.write( "A = 340° is in QIV and has reference angle 360°-340° = 20°\r\n" );
document.write( "thus sin(340°) = -sin(20°)\r\n" );
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document.write( "A/2 = 170° is in QII and has reference angle 180°-170° = 10°\r\n" );
document.write( "thus sin(170°) = sin(10°)\r\n" );
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document.write( "And we know that sin(20°) > sin(10°))\r\n" );
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document.write( "We put question marks for the signs + or - to\r\n" );
document.write( "include all choices A), B), C), D)\r\n" );
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document.write( "2sin(170°) = ? √(1+sin340°) ? √(1-sin340°)\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "2sin(10°) = ?√(1-sin(20°) ? √(1+sin(20°)\r\n" );
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document.write( "Since √(1+sin(20°) has the larger absolute value it must be\r\n" );
document.write( "positive.  So B) and C) are eliminated.\r\n" );
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document.write( "2sin(10°) = ?√(1-sin(20°) + √(1+sin(20°) \r\n" );
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document.write( "We square both sides:\r\n" );
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document.write( "4sinē(10°) = 1 -sin(20°) ? 2√(1-sin(20°))√(1+sin(20°)) + 1+sin(20°)\r\n" );
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document.write( "Note that the ? did not change in the squaring process.\r\n" );
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document.write( "4sinē(10°) = 2  ?  2√(1-sinē(20°)) \r\n" );
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document.write( "2sinē(10°) = 1  ?  √cosē(20°)\r\n" );
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document.write( "2sinē(10°) = 1  ?  √cosē(20°)\r\n" );
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document.write( "There is an Identity which states:\r\n" );
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document.write( "\"cos%5E%22%22%282theta%29=1-2sin%5E2%28theta%29\"\r\n" );
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document.write( "thus\r\n" );
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document.write( "\"2sin%5E2%28theta%29=1-cos%5E%22%22%282theta%29\"\r\n" );
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document.write( "Therefore the ? must be -\r\n" );
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document.write( "Therefore the only correct choice is D).\r\n" );
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document.write( "Edwin
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