Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a strictly decreasing function with $|f(t)| \lt \pi / 2$ for all $t \in \mathbf{R}$. Let $g:[0, \pi] \rightarrow \mathbf{R}$ be a function defined by $g(t)=\sin (f(t))$. Which one of the following statements is Correct?

• A

  $g$ is decreasing on $(0, \pi / 2)$ and increasing on $(\pi / 2, \pi)$.
• B

  $g$ is increasing on $[0, \pi]$.
• Correct answer
  C

  $g$ is decreasing on $[0, \pi]$.
• D

  $g$ is increasing on $(0, \pi / 2)$ and decreasing on $(\pi / 2, \pi)$.

Hence, the correct answer is option: 'C'.