Question

If $\tan \theta =0.4$, when $\theta$ lies between $0^o$ and ${360}^o$, write down the possible values of $\theta$ and $\sin \theta$.

Answer 1

Given:

$\tan \theta =0.4$

$\theta =n\pi +{\tan }^{-1}\left(0.4\right)$

Now, values of $n$ can be find by substituting $n=1,2,\mathrm{3.....}$ and matching with the table.

Again,

$\tan \theta =0.4=\frac{2}{5}$

$\Rightarrow \sin \theta =\frac{2}{\sqrt{{\left(5\right)}^2-{\left(2\right)}^2}}=\frac{2}{\sqrt{25-4}}=\frac{2}{\sqrt{21}}$

Hence, this is the required result.