Chapter 13 - The Trigonometric Functions - 13.1 Definitions of the Trigonometric Functions - 13.1 Exercises - Page 678: 43

$\sec 225^\circ=-\sqrt 2$

We are given $\sec \frac{5\pi}{4}$ convert $\frac{5\pi}{4}$ to degrees $\frac{5\pi}{4}$ radians=$\frac{5\pi}{4}(\frac{180^\circ}{\pi})$ $\frac{5\pi}{4}$ radians= $225^\circ$ $\sec 225^\circ=-sec 45^\circ $ and $\sec \theta=\frac{1}{\cos \pi}$ so $\sec 225^\circ=-\sqrt 2$