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Q.
The range of $f(x)=\cos \frac{\pi[x]}{2}$ is
Trigonometric Functions
Solution:
$\because[x]$ is an integer, $\cos (-x)=\cos \,x$ and
$\cos \left(\frac{\pi}{2}\right)=0, \cos 2\left(\frac{\pi}{2}\right)=-1, \cos 0\left(\frac{\pi}{2}\right)=1, \cos 3\left(\frac{\pi}{2}\right)=0$
Hence range $=\{-1,0,1\}$