Question

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

Answer 1

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

Explanation:

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`