Chapter 13, Trigonometric Ratios and Functions - 13.4 Evaluate Inverse Trigonometric Functions - 13.4 Exercises - Quiz for Lessons 13.3-13.4 - Page 880: 11

$30^{\circ}$ or, $\dfrac{\pi}{6}$

Here, we have $\tan^{-1} (\dfrac{\sqrt 3}{3})$ This means that $\theta=\tan^{-1} (\dfrac{\sqrt 3}{3})$ This gives : $\theta=30^{\circ}$ The range of the function $arccos$ is from $[-90^{\circ}, 90^{\circ}]$. Hence, we have $\theta=30^{\circ}$ or, $\dfrac{\pi}{6}$