document.write( "Question 922044: find the exact solutions to the equation tan x = -1/(square root of 3) on the interval zero is less than or equal to x is less than or equal to 2pi \n" ); document.write( "

Algebra.Com's Answer #559484 by KMST(5328) $\"\"$ $\"About$

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We know that $\"tan%2830%5Eo%29=1%2Fsqrt%283%29=sqrt%283%29%2F3\"$ ,
\n" ); document.write( "and if we are expected to measure angles in radians,
\n" ); document.write( " $\"tan%28pi%2F6%29=1%2Fsqrt%283%29=sqrt%283%29%2F3\"$ , so we have one solution, $\"highlight%28x=pi%2F6%29%29\"$ .
\n" ); document.write( "We also know that tangent is a function with a period of $\"pi\"$ ,
\n" ); document.write( "and as $\"pi%2F6%2Bpi=7pi%2F6\"$ ,
\n" ); document.write( " $\"tan%28pi%2F6%29=tan%28pi%2F6%2Bpi%29=tan%287pi%2F6%29\"$ ,
\n" ); document.write( "so $\"highlight%28x=7pi%2F6%29\"$ is another solution.
\n" ); document.write( "There are no other solutions.
\n" ); document.write( "There are infinity of other angles with the same tangent,
\n" ); document.write( "such as $\"-5pi%2F6=pi%2F6-pi\"$ or $\"13pi%2F6=pi%2F6%2B2pi\"$ ,
\n" ); document.write( "but those are not in the interval $\"0%3C=x%3C=2pi\"$ \n" ); document.write( "

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