Exponential and trigonometric functions practice question 14

The limit has the shape of a difference quotient. Which function $f$ and which point $a$ would make it $\dfrac{f(x) - f(a)}{x - a}$?

$\tfrac{1}{2} = \sin\tfrac{\pi}{6}$. Compare with $f'(a) = \lim_{x \to a}\dfrac{f(x) - f(a)}{x - a}$.

With $f(x) = \sin x$ and $a = \pi/6$, the limit is $f'(\pi/6)$. Differentiate sine, then evaluate at $\pi/6$.