document.write( "Question 771979: how to find exact value of sin(cos^-1(-1/3)) \n" ); document.write( "

Algebra.Com's Answer #470629 by Edwin McCravy(20063) $\"\"$ $\"About$

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document.write( "sin[cos^-1()]\r\n" );
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document.write( "First we find the angle cos^-1()\r\n" );
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document.write( "The inverse cosine of a negative number is in quadrant II\r\n" );
document.write( "between 90° or  and 180° or p.\r\n" );
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document.write( "We'll draw the picture of the angle cos^-1() in quadrant\r\n" );
document.write( "II.\r\n" );
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document.write( "Since the cosine is  =  we take x\r\n" );
document.write( "as the numerator of , x=-1, and the r as the denominator,\r\n" );
document.write( "3, r=3:\r\n" );
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document.write( "Then we calculate y by the Pythagorean theorem \r\n" );
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document.write( "   x² + y² = r²\r\n" );
document.write( "(-1)² + y² = 3²\r\n" );
document.write( "    1 + y² = 9\r\n" );
document.write( "        y² = 8\r\n" );
document.write( "         y = √8\r\n" );
document.write( "         y = √4·2\r\n" );
document.write( "         y = 2√2\r\n" );
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document.write( "Therefore sin[cos^-1()] =  =  = .   \r\n" );
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document.write( "Edwin

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