Question

If $\sin \theta =-\frac{4}{5}$ and $\pi <\theta <\frac{3\pi }{2}$, then $\tan \theta +\cos \theta =$

• A. $\frac{11}{15}$
• B. $-\frac{11}{15}$
• C. $\frac{9}{25}$
• D. $-\frac{9}{25}$

Answer 1

The correct option is A $\frac{11}{15}$

Using ${\sin }^2\theta +{\cos }^2\theta =1,$
$\sin \theta =-\frac{4}{5}\Rightarrow {\cos }^2\theta =1-\frac{16}{25}=\frac{9}{25}$
$\Rightarrow \cos \theta =\pm \frac{3}{5}$
$\because \theta \in 3^{rd}$ quadrant
$\cos \theta =-\frac{3}{5}$
and
$\tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{4}{3}$
So $\tan \theta +\cos \theta =\frac{11}{15}$