Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 260: 111c

$15^{\circ}$

To find the value of $\theta$, we need to substitute the value of $x=3$ in the equation and solve; $\theta=\tan^{-1}(\frac{x}{x^{2}+2})$ $\theta=\tan^{-1}(\frac{3}{3^{2}+2})$ $\theta=\tan^{-1}(\frac{3}{9+2})$ $\theta=\tan^{-1}(\frac{3}{11})$ $\theta=15.3\approx15^{\circ}$