Question

If $\tan \theta =\frac{4}{3}$, then $\sin \theta =$

• A. $\frac{3}{4}$
• B. $\frac{3}{5}$
• C. $\frac{4}{5}$
• D. $\frac{5}{3}$
• E. $\frac{5}{4}$

Answer 1

The correct option is C $\frac{4}{5}$

Given, $\tan \theta =\frac{4}{3}$

$\Rightarrow \frac{\sin \theta }{\cos \theta }=\frac{4}{3}$

$\Rightarrow \cos \theta =\frac{3}{4}\sin \theta$

$\Rightarrow {\sin }^2\theta =1-{\cos }^2\theta ({\sin }^2\theta +{\cos }^2\theta =1)$

$\Rightarrow {\sin }^2\theta =1-\frac{9}{16}{\sin }^2\theta$

$\Rightarrow {\sin }^2\theta +\frac{9}{16}{\sin }^2\theta =1$

$\Rightarrow \frac{25}{16}{\sin }^2\theta =1$

$\Rightarrow {\sin }^2\theta =\frac{16}{25}$

$\Rightarrow \sin \theta =\frac{4}{5}$