document.write( "Question 1081528: If sinx = 15/17 an X is in quadrant 1, find the exact values of sin X/2 and cos x/2 \n" ); document.write( "
Algebra.Com's Answer #695624 by ikleyn(52796)\"\" \"About 
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\n" ); document.write( "If sinx = 15/17 an X is in quadrant 1, find the exact values of sin X/2 and cos x/2
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\n" ); document.write( "\n" ); document.write( "The standard technique for solving such problems is THIS:\r
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document.write( "1.  cos(x) = \"sqrt%281-sin%5E2%28x%29%29\" = \"sqrt%281-%2815%2F17%29%5E2%29\" = \"sqrt%281+-+225%2F289%29\" = \"sqrt%28%28289-225%29%2F289%29\" = \"sqrt%2864%2F289%29\" = \"8%2F17\"\r\n" );
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document.write( "    notice sqrt is taken with the sign \"+\" since the angle \"x\" is in Q1 by the condition.\r\n" );
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document.write( "2.  Now  \"sin%28x%2F2%29\" =    (apply the Trigonometry formula for half-argument)\r\n" );
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document.write( "         = \"sqrt%28%281-cos%28x%29%29%2F2%29\" = \"sqrt%28%281-8%2F17%29%2F2%29\" = \"sqrt%28%2817-8%29%2F%2817%2A2%29%29\" = \"sqrt%289%2F34%29\" = \"3%2Fsqrt%2834%29\" = \"%283%2Asqrt%2834%29%29%2F34\".\r\n" );
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document.write( "    Again, the sign is \"+\" at the sqrt since x/2 is in Q1 together with x.\r\n" );
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document.write( "3.  Next  \"cos%28x%2F2%29\" =    (apply the Trigonometry formula for half-argument)\r\n" );
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document.write( "         = \"sqrt%28%281%2Bcos%28x%29%29%2F2%29\" = \"sqrt%28%281%2B8%2F17%29%2F2%29\" = \"sqrt%28%2817%2B8%29%2F%2817%2A2%29%29\" = \"sqrt%2825%2F34%29\" = \"5%2Fsqrt%2834%29\" = \"%285%2Asqrt%2834%29%29%2F34\".\r\n" );
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document.write( "    Again, the sign is \"+\" at the sqrt since x/2 is in Q1 together with x.\r\n" );
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document.write( "For half-argument formulas of Trigonometry see the lessons\r\n" );
document.write( "    - FORMULAS FOR TRIGONOMETRIC FUNCTIONS\r\n" );
document.write( "    - Trigonometric functions of half argument\r\n" );
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