How do you find the exact value of $tan ((7pi)/6)$ ?

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Answer 1 · 2016-04-13T03:47:48

$tan((7pi)/6)=1/sqrt3$

The trigonometric function $tanx$ has a periodicity of $pi$ , which means it repeats its values after each $pi$ .

Mathematically we can say that $tan(npi+x)=tanx$ for all integers $n$ .

Hence, $tan((7pi)/6)=tan(pi+(pi/6))=tan(pi/6$

But as $tan(pi/6)=tan30^o=1/sqrt3$ ,

Hence, $tan((7pi)/6)=1/sqrt3$

How do you find the exact value of tan ((7pi)/6) tan ((7pi)/6)?