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

$18^{\circ}$

To find the value of $\theta$, we need to substitute the value of $x=2$ in the equation and solve; $\theta=\tan^{-1}(\frac{x}{x^{2}+2})$ $\theta=\tan^{-1}(\frac{2}{2^{2}+2})$ $\theta=\tan^{-1}(\frac{2}{4+2})$ $\theta=\tan^{-1}(\frac{2}{6})$ $\theta=\tan^{-1}(\frac{1}{3})$ $\theta=18.4\approx18^{\circ}$