Answer
$1$
Work Step by Step
Consider the tangent line that contains the point $(x, c)$. The slope the tangent line to the graph of $f(x)$ at $(x, c)$ can be written as
$f'(x) =\lim\limits_{x \to c} \dfrac{f(x)-f(c)}{x-c}$
Consider $c=0$ and $f(x)=\sin x$. Thus, we have:
$f'(0) =\lim\limits_{x \to 0} \dfrac{f(x)-f(0)}{x-0} \\=\lim\limits_{x \to 0} \dfrac{\sin x -\sin 0}{x}\\=\lim\limits_{x \to 0} \dfrac{\sin x }{x}\\=1$
