## Calculus (3rd Edition)

$f(x)=\sin x$ and $a=\frac{\pi}{6}$
The definition of derivative at point $a$ is $f'(a)=\lim\limits_{h \to 0}\frac{f(a+h)-f(a)}{h}$ But given that $f'(a)=\lim\limits_{h \to 0}\frac{\sin(\frac{\pi}{6}+h)-0.5}{h}$ $\implies f(a+h)=\sin(\frac{\pi}{6}+h)$ and $f(a)=0.5=\sin \frac{\pi}{6}$ which gives $f(x)=\sin x$ and $a=\frac{\pi}{6}$.