Question

The range of f(x) = cos [x], for π/2 < x < π/2 is

(a) {−1, 1, 0}
(b) {cos 1, cos 2, 1}
(c) {cos 1, −cos 1, 1}
(d) [−1, 1]

Answer 1

(b) {cos 1, cos 2, 1}

Since, f(x) = cos [x], where $\frac{-\mathrm{\pi }}{2}<x<\frac{\mathrm{\pi }}{2}$,
$$\begin{gathered} -\frac{\mathrm{\pi }}{2}<x<\frac{\mathrm{\pi }}{2} \\ \Rightarrow -1.57<x<1.57 \\ \Rightarrow \left[x\right]\in \{-1,0,1,2\} \\ \mathrm{Thus},\cos \left[x\right]=\{\cos (-1),\cos 0,\cos 1,\cos 2\} \\ \mathrm{Range}\mathrm{of}f\left(x\right)=\{\cos 1,1,\cos 2\} \end{gathered}$$