document.write( "Question 1201910: cot(arccos-square root 6/3)\r
\n" ); document.write( "\n" ); document.write( "I know triangle is in quadrant II because of negative sign.\r
\n" ); document.write( "\n" ); document.write( "Just confused on how the answer is -square root 2.
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Algebra.Com's Answer #836487 by greenestamps(13203)\"\" \"About 
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\n" ); document.write( "The range of the arccos function is from 0 to pi (radians), or 0 to 180 degrees, so the angle is in quadrant I or II.

\n" ); document.write( "Then, since the cosine is negative, the angle is in quadrant II.

\n" ); document.write( "You have gotten that far in your work.

\n" ); document.write( "From there, you can use \"sin%5E2%28x%29%2Bcos%5E2%28x%29=1\" to find the sine of the angle, choosing the positive answer because the angle is in quadrant II, where sine is positive.

\n" ); document.write( "\"sin%5E2%28x%29%2B%28-sqrt%286%29%2F3%29%5E2=1\"
\n" ); document.write( "\"sin%5E2%28x%29%2B6%2F9=1\"
\n" ); document.write( "\"sin%5E2%28x%29=1%2F3\"
\n" ); document.write( "\"sin%28x%29=1%2Fsqrt%283%29=sqrt%283%29%2F3\"

\n" ); document.write( "Then use \"cot%28x%29=cos%28x%29%2Fsin%28x%29\" to find the answer to the problem.

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