Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises - Page 61: 82

$\theta=135^{\circ}$ or $225^{\circ}$

1. Since $sec\theta$ is negative, $\theta$ must be in quadrant II or III. 2. The absolute value of $sec\theta$ is $\sqrt 2$, therefore the reference angles is $45^{\circ}$. The actual angles in II and III quadrants are following: $180^{\circ}-45^{\circ}=135^{\circ}$ $180^{\circ}+45^{\circ}=225^{\circ}$