Question

Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .

 

Answer 1

Since f(x) = cos [x], where

\[\frac{- \pi}{2} < x < \frac{\pi}{2}\] ,

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