document.write( "Question 825765: If csc theta = 2/√3, P theta is in 2 Q, then cos theta is equal to:\r
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Algebra.Com's Answer #497571 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
If $\"csc%28theta%29+=+2%2Fsqrt%283%29%2C+%7B%7B%7BP%28theta%29\"$ is in Q2, then $\"cos%28theta%29\"$ is equal to:
\n" ); document.write( "a) -√3/2
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\n" ); document.write( "c) 3/4
\n" ); document.write( "d) -3/4
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document.write( "It's none of those answers.  I'll do it two ways to show that the\r\n" );
document.write( "correct answer is , as the other tutor has just flatly \r\n" );
document.write( "stated with no explanation.  (BTW, a tutor should do more than give\r\n" );
document.write( "answers. Too many teachers know their subject but can't teach it!).\r\n" );
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document.write( "First way:\r\n" );
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document.write( "Draw the picture of angle  in the second quadrant Q2. \r\n" );
document.write( "Since the cosecant is hypotenuse/opposite or r/y, and since we are given \r\n" );
document.write( ", make r=2 and y=, and calculate x using the \r\n" );
document.write( "Pythagorean theorem:\r\n" );
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document.write( "    x²+y² = r²\r\n" );
document.write( "x²+ = 2²\r\n" );
document.write( "    x²+3 = 4\r\n" );
document.write( "      x² = 1\r\n" );
document.write( "       x = ±√1\r\n" );
document.write( "       x = ±1, we take x = -1 \r\n" );
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document.write( "We take x negative because it goes left from the origin, \r\n" );
document.write( "and we ALWAYS take r positive because it begins on the\r\n" );
document.write( "right side of the x-axis and doesn't change its sign when\r\n" );
document.write( "it swings around into the other quadrants. \r\n" );
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document.write( "We want .  The cosine is adjacent/hypotenuse or x/r,\r\n" );
document.write( "so \r\n" );
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document.write( "Second way, using these identities:\r\n" );
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document.write( "1.  \r\n" );
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document.write( "2.  \r\n" );
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document.write( "Using 1.,\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "Using 2.,\r\n" );
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document.write( "Since the cosine is negative in the second quadrant Q2,\r\n" );
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document.write( "              \r\n" );
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document.write( "Edwin

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