Recall that $\arcsin(t)$ (also known as $\sin^{-1}(t)$) is a function with domain $[-1,1]$ and range $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$. Consider the function $f(x) := \arcsin(\sin(x))$ and answer the following questions as a series of four letters (T for True and F for False) in order.
(a) The function $f(x)$ is well defined for all real numbers $x$.
(b) The function $f(x)$ is continuous wherever it is defined.
(c) The function $f(x)$ is differentiable wherever it is continuous.