document.write( "Question 42656: Find the exact value of sin θ/2 if cos θ = 2/3 and 270° < θ <360°. \r
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Algebra.Com's Answer #27755 by AnlytcPhil(1807)\"\" \"About 
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Find the exact value of sin θ/2 if cos θ = 2/3 and 270° < θ < 360°.\r\n" );
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document.write( "Use the formula \r\n" );
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document.write( "sin(θ/2) = ±Ö(1-cosθ)/2\r\n" );
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document.write( "Where the sign of the sine is taken according to which quadrant x\r\n" );
document.write( "is in.\r\n" );
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document.write( "It is unfortunate that the words \"sine\" and \"sign\" are homophones,\r\n" );
document.write( "because it sounds funny and is often confusing to speak of \"the\r\n" );
document.write( "sign of the sine\".  Some teachers use \"positiveness or\r\n" );
document.write( "negativeness of the sine\" instead of \"sign of the sine\".\r\n" );
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document.write( "Anyway, substitute 2/3 for cosθ in the formula:\r\n" );
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document.write( "sin(θ/2) = ±Ö(1-2/3)/2 \r\n" );
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document.write( "Change the last \"/\" to a \"÷\"\r\n" );
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document.write( "sin(θ/2) = ±Ö(1/3)÷2 \r\n" );
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document.write( "Change the 2 to 2/1\r\n" );
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document.write( "sin(θ/2) = ±Ö(1/3)÷(2/1)\r\n" );
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document.write( "Invert and multiply to perform the divion under\r\n" );
document.write( "the radical:\r\n" );
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document.write( "sin(θ/2) = ±Ö(1/3)×(1/2) \r\n" );
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document.write( "sin(θ/2) = ±Ö1/6\r\n" );
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document.write( "Now we have to determine whether to use the + or\r\n" );
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document.write( "We are givem:\r\n" );
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document.write( "270° < θ < 360°\r\n" );
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document.write( "so we whii divide all three sides of that by 2\r\n" );
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document.write( "(270/2)° < θ/2 < (360/2)°\r\n" );
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document.write( " 135° < θ/2 < 180°\r\n" );
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document.write( "This tells us that θ/2 is in quadrant II.\r\n" );
document.write( "The sine is positive in the second quadrant\r\n" );
document.write( "Therefore we know that  sin(θ/2) is positive,\r\n" );
document.write( "So\r\n" );
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document.write( "sin(θ/2) = Ö1/6\r\n" );
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document.write( "Your teacher may want you to rationalize the\r\n" );
document.write( "denominator and get\r\n" );
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document.write( "sin(θ/2) = Ö6/6\r\n" );
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document.write( "Edwin
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