Question

If $\sin x=-\frac{24}{25}$, then the value of $\tan x$ is

• A. $\frac{24}{25}$
• B. $\frac{-24}{7}$
• C. $\frac{25}{24}$
• D. None of these

Answer 1

The correct option is B $\frac{-24}{7}$

The correct option is B

We have,

$sinx=-\frac{24}{25}$

We know that

$cosx=\sqrt{1-si{n}^{2}x}$

$=\sqrt{1-(\frac{-24}{25}{)}^2}$

$=\sqrt{\frac{625-576}{625}}$

$=\sqrt{\frac{49}{625}}$

$=\frac{7}{25}$

Thus

$tanx=\frac{sinx}{cosx}=\frac{\frac{-24}{25}}{\frac{7}{25}}$

$tanx=\frac{-24}{7}$