document.write( "Question 787558: Give a general solution in radians using the unit circle
\n" ); document.write( "3 tan of x minus the square root of three equals zero
\n" ); document.write( "3 tan of x equals the square root of three
\n" ); document.write( "tan of x equals square root of 3 over 3
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Algebra.Com's Answer #478243 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3tan%28x%29-sqrt%283%29=0\"$
\n" ); document.write( " $\"3tan%28x%29=sqrt%283%29\"$
\n" ); document.write( " $\"tan%28x%29=sqrt%283%29%2F3\"$
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\n" ); document.write( "We know that $\"tan%28pi%2F6%29=sqrt%283%29%2F3\"$ (or $\"tan%2830%5Eo%29=sqrt%283%29%2F3\"$ if using degrees). For that angle $\"sin%28pi%2F6%29=1%2F2\"$ and $\"cos%28pi%2F6%29=sqrt%283%29%2F2\"$
\n" ); document.write( "That is the only solution for $\"-pi%2F2%3Cx%3Cpi%2F2\"$ (or $\"-90%5Eo%3Cx%3C90%5Eo\"$ if using degrees).
\n" ); document.write( "The function does not exist for $\"x=-pi%2F2\"$ or $\"x=pi%2F2\"$ , where $\"cos%28x%29=0\"$ .
\n" ); document.write( "In between those values $\"tan%28x%29\"$ increases continuously.
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\n" ); document.write( "We also know that if $\"tan%28x%29\"$ exists, $\"tan%28x%2Bpi%29=tan%28x%29\"$ , so the funcion's values repeat at $\"pi\"$ intervals, and we say that the function has period $\"pi\"$ .
\n" ); document.write( "So there are infinite solutions that can be all expressed as
\n" ); document.write( " $\"highlight%28x=pi%2F6%2Bk%2Api%29\"$ for all $\"k\"$ integers (or $\"highlight%28x=30%5Eo%2Bk%2A180%5Eo%29\"$ for all $\"k\"$ integers if you measure angles in degrees). \n" ); document.write( "

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