Calculus: Early Transcendentals 8th Edition

$-\frac{\sqrt{3}}{2}$
$\lim\limits_{\theta \to \pi/3}\frac{cos~\theta-0.5}{\theta-\pi/3}$ This is an expression for the derivative of $~~f(\theta) = cos~\theta~~$ evaluated at the point $\theta = \frac{\pi}{3}$ We can evaluate the derivative: $f(\theta) = cos~\theta$ $f'(\theta) = -sin~\theta$ $f'(\frac{\pi}{3}) = -sin~\frac{\pi}{3}$ $f'(\frac{\pi}{3}) = -\frac{\sqrt{3}}{2}$