Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$0.444 \text{ radians}$
$\because A = \dfrac{1}{2}r^2 \theta$ where $r$: Radius of the circle $\theta$: Central angle that subtends the arc (in radians) $A$: Area of the sector of the circle formed by the central angle $\theta$ Derive the formula for $\theta$: \begin{align*} A&=\frac{1}{2}r^2\theta\\\\ 2A&=r^2\theta\\\\ \dfrac{2A}{r^2}&=\theta\\\\ \end{align*} Using this formula gives: $\theta = \dfrac{2 A}{r^2}$ $\theta = \dfrac{2\times 8}{6^2} = \boxed{0.444 \text{ radians}}$