# How do you evaluate tan^-1(tan((19pi)/10))?

Jul 21, 2016

$\left(\frac{19}{10}\right) \pi$.

#### Explanation:

${\tan}^{- 1} \tan \left(\frac{19 \pi}{10}\right)$ is

the angle whose tangent is $\tan \left(\frac{19 \pi}{10}\right)$

$= \left(\frac{19}{10}\right) \pi$.

From the definitions of successive operations

$f {f}^{- 1} \left(y\right) = y$ and

${f}^{- 1} f \left(x\right) = x ,$

only the operand value has to be given as the answer and

not any other value, from the general value

$n \pi + \frac{19 \pi}{10} , n = 0 , \pm 1 , \pm 2 , \pm 3. \ldots$

Here, $f = \tan \mathmr{and} {f}^{- 1} = {\tan}^{- 1}$.