Chapter 13, Trigonometric Ratios and Functions - 13.4 Evaluate Inverse Trigonometric Functions - 13.4 Exercises - Quiz for Lessons 13.3-13.4 - Page 880: 14

$260.54^{\circ}$

Here, we have $\sin^{-1} (6)$ The angle $\theta$ is in the First quadrant. This means that $\theta=\tan^{-1} (6) \approx 80.54^{\circ}$ We want an angle in the Third quadrant: Then we have $\theta=\theta'+180^{\circ}=80.54^{\circ}+180^{\circ}=260.54^{\circ}$