# How do you evaluate Tan (sin^-1 (2/3)) ?

Nov 12, 2016

#### Answer:

Conventional value is $\frac{2}{\sqrt{5}}$ and the general value is $\pm \frac{2}{\sqrt{5}}$.

#### Explanation:

Let $a = {\sin}^{- 1} \left(\frac{2}{3}\right) \in {Q}_{1}$ for the conventional principal value and

also $\in {Q}_{2}$, for the general value.

The given expression is tan a

$= \sin \frac{a}{\cos} a = \frac{\frac{2}{3}}{\pm \sqrt{1 - {\left(\frac{2}{3}\right)}^{2}}} = \pm \frac{2}{\sqrt{5}}$.

Conventional value is $\frac{2}{\sqrt{5}}$ and the general value is $\pm \frac{2}{\sqrt{5}}$.