Chapter 13 - Periodic Functions and Trigonometry - 13-2 Angles and the Unit Circle - Practice and Problem-Solving Exercises - Page 841: 42

$$45^\circ,-315^\circ$$

Angles coterminal to angle $\theta$ are given by $\theta \pm n\times360^\circ$ where n is an integer. Therefore, an angle coterminal with $-675^\circ$ that is positive is $$-675^\circ + (2)360^\circ = -675^\circ+720^\circ = 45^\circ$$ and an angle coterminal with $-675^\circ$ that is negative is $$-675^\circ + (1)360^\circ = -315^\circ$$