Question

If $\sin a=\frac{3}{7}$ and $\cos a<0$, what is the value of $\tan a$

• A. $\frac{-\left(3\sqrt{20}\right)}{10}$
• B. $\frac{-\left(\sqrt{10}\right)}{10}$
• C. $\frac{-\left(3\sqrt{10}\right)}{20}$
• D. $\frac{\left(2\sqrt{5}\right)}{10}$

Answer 1

The correct option is C $\frac{-\left(3\sqrt{10}\right)}{20}$

Given, $\sin a=\frac{3}{7}$
$\Rightarrow \cos a=\sqrt{1-{\sin }^{2}a}=\sqrt{1-{\left(\frac{3}{7}\right)}^2}=\sqrt{\frac{40}{49}}=-\frac{2\sqrt{10}}{7}$
$\Rightarrow \tan a=\frac{\sin a}{\cos a}=-\frac{\frac{3}{7}}{\frac{2\sqrt{10}}{7}}=-\frac{3}{2\sqrt{10}}$