Question

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

Options

• (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 \[\frac{- \pi}{2} < x < \frac{\pi}{2}\]

\[- \frac{\pi}{2} < x < \frac{\pi}{2}\]
\[ \Rightarrow - 1 . 57 < x < 1 . 57\]
\[ \Rightarrow [x] \in { - 1, 0, 1, 2}\]
\[\text{ Thus } , \cos [x] = {\cos ( - 1), \cos 0, \cos1, \cos 2 }\]
\[\text{ Range of } f(x) = {\cos 1, 1, \cos 2}\]