Question

Write the range of the funciton $f\left(x\right)=sin\left[x\right]$, where $\frac{-\pi }{4}\le x\le \frac{\pi }{4}$.

Answer 1

We have,
$f\left(x\right)=sin\left[x\right]$, where $\frac{-\pi }{4}\le x\le \frac{\pi }{4}$
Now,
$\left[x\right]=\{\begin{array}{cc}0,& x=\frac{\pi }{4}\\ -1& x=\frac{-\pi }{4}\end{array}$
$\therefore sin\left\{x\right\}=\{\begin{array}{cc}0,& x-\frac{\pi }{4}\\ -sin1& x=\frac{-\pi }{4}\end{array}$
$\therefore$ Range (sin[x]) $=\{-sin1,0,sin1\}$