Answer
$\sqrt 2$
Work Step by Step
sec(-$\frac{9\pi}{4}$) = sec $\frac{9\pi}{4}$
sec($\frac{\pi}{4}$ + 2$\pi$) = sec$\frac{\pi}{4}$
sec $\frac{\pi}{4}$=$\frac{1}{cos \frac{\pi}{4}}$
sec $\frac{\pi}{4}$ =$\frac{1}{\frac{\sqrt 2}{2}}$ = $\sqrt 2$