# How do you use the properties of inverse trigonometric functions to evaluate tan(arcsin (0.31))?

Nov 25, 2014

Let

$\theta = \arcsin \left(0.31\right)$

by rewriting in terms of sine,

$\sin \theta = 0.31 = \frac{O}{H} \implies$ Let $\left\{\begin{matrix}O = 0.31 \\ H = 1\end{matrix}\right.$

By Pythagorean Theorem,

$A = \sqrt{{H}^{2} - {O}^{2}} = \sqrt{{1}^{2} - {\left(0.31\right)}^{2}} = \sqrt{0.9039}$

Hence,

$\tan \left(\arcsin \left(0.31\right)\right) = \tan \theta = \frac{O}{A} = \frac{0.31}{\sqrt{0.9039}}$

I hope that this was helpful.