Question

If $\cos \theta =-\frac{7}{25}$ and $\pi <\theta <\frac{3\pi }{2}$, then $\tan \theta$ is equal to

• A. $-\frac{25}{7}$
• B. $\frac{25}{7}$
• C. $-\frac{24}{7}$
• D. $\frac{24}{7}$

Answer 1

The correct option is D $\frac{24}{7}$

$\cos \theta =-\frac{7}{25}\Rightarrow \sec \theta =-\frac{25}{7}$
$\Rightarrow {\tan }^2\theta =({\sec }^2\theta -1)(\because {\tan }^2\theta +1={\sec }^2\theta )=\frac{625}{49}-1=\frac{576}{49}$
$\Rightarrow \tan \theta =\pm \frac{24}{7}$
$\therefore \tan \theta =\frac{24}{7}(\because \pi <\theta <\frac{3\pi }{2})$