Question

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

Answer 1

Given : f(x) = sin [x], where $\frac{-\mathrm{\pi }}{4}\le x\le \frac{\mathrm{\pi }}{4}$.
$$\begin{gathered} -\frac{\mathrm{\pi }}{4}\le x\le \frac{\mathrm{\pi }}{4} \\ \Rightarrow -7.85\le x\le 0.785 \\ \therefore x\in \left[-7.85,7.85\right] \\ \text{Or}x=\{0,1\} \\ \mathrm{Thus},\mathrm{range}\mathrm{of}f\left(x\right)=\sin \left[x\right]\mathrm{is} \\ \{\sin 0,\sin 1\}=\{0,\sin 1\} \end{gathered}$$