Question

The range of $f\left(x\right)=cos\left[x\right]$, for $-\frac{\pi }{2}<x<\frac{\pi }{2}$ is

• A. {-1, 1, 0}
• B. {cos 1, cos 2, 1}
• C. {cos 1, - cos 1, 1}
• D. [-1, 1]

Answer 1

The correct option is B

{cos 1, cos 2, 1}

{cos 1, cos 2, 1}
Since, $f\left(x\right)=cos\left[x\right]$, where $\frac{-\pi }{2}<x<\frac{\pi }{2}$, $-\frac{\pi }{2}<x<\frac{\pi }{2}\Rightarrow -1.57<x<1.57\Rightarrow \left[x\right]ϵ\{-1,0,1,2\}$. Thus, $cos\left[x\right]=\left\{cos\right(-1),cos0,cos1,cos2\}$. Range of $f\left(x\right)=\{cos1,1,cos2\}$