Find the Range of the Function
Question:
Write the range of the function
\[ f(x)=\sin[x] \]
where
\[ -\frac{\pi}{4}\le x\le \frac{\pi}{4} \]
Solution:
Since
\[ -\frac{\pi}{4}\le x\le \frac{\pi}{4} \]
we have
\[ -1\le [x]\le0 \]
Therefore,
\[ [x]=-1 \quad \text{or} \quad 0 \]
Hence,
\[ f(x)=\sin(-1),\ \sin0 \]
\[ =-\sin1,\ 0 \]
Therefore, range is
\[ \boxed{\{-\sin1,\ 0\}} \]