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.
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #836491 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"cot%28arccos%28-%28sqrt%286%29%29%2F3%29%5E%22%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "First look only at \r\n" );
document.write( "\r\n" );
document.write( "\"arccos%28-%28sqrt%286%29%29%2F3%29\"\r\n" );
document.write( "\r\n" );
document.write( "That asks: What angle between 0 and 360 has \"-%28sqrt%286%29%29%2F3\" for its cosine?\r\n" );
document.write( "\r\n" );
document.write( "It's a NEGATIVE cosine and the cosine is negative only in QII and QIII.\r\n" );
document.write( "\r\n" );
document.write( "So it's got to be one of these two:\r\n" );
document.write( "\r\n" );
document.write( "   \r\n" );
document.write( "\r\n" );
document.write( "The first one is the PRINCIPLE value, since it has the lesser absolute\r\n" );
document.write( "value. (The shorter red arc). So we calculate the other side of the triangle \r\n" );
document.write( "for the first one, using the Pythagorean theorem:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We choose the positive sign, since it goes up.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's the picture of\r\n" );
document.write( "\r\n" );
document.write( "\"arccos%28-%28sqrt%286%29%29%2F3%29\"\r\n" );
document.write( "\r\n" );
document.write( "And we want \r\n" );
document.write( "\r\n" );
document.write( "\"cot%28arccos%28-%28sqrt%286%29%29%2F3%29%5E%22%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "Since we know that \"cotangent=adjacent%2Fopposite\",\r\n" );
document.write( "\r\n" );
document.write( "the answer is\r\n" );
document.write( "\r\n" );
document.write( "\"%28-sqrt%286%29%29%2F%28sqrt%283%29%29\"\"%22%22=%22%22\"\"-sqrt%286%2F3%29\"\"%22%22=%22%22\"\"-sqrt%282%29\".\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );