Question

If $\sec \alpha =\frac{13}{5}$ where ${270}^o<\alpha <{360}^o$, then what is $\sin \alpha$ equal to?

• A. $5/13$
• B. $12/13$
• C. $-12/13$
• D. $-13/12$

Answer 1

The correct option is C $-12/13$

$\sec \alpha =\frac{13}{5}\cos \alpha =\frac{5}{13}$
In the given range, $\sin$ is negative
So, $\sin \alpha =\frac{-\sqrt{{13}^2-5^2}}{13}=-\frac{12}{13}$
Hence, option C is correct