Write the range of the function f(x)= [x], where - 4 x 4 . - Vidyadip

Question

Write the range of the function $f(x)=\sin [x]$, where $\frac{-\pi}{4} \leq x \leq \frac{\pi}{4}$.

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Answer

From the given question ,
we can write, $f(x)=\sin (x)$
$-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}$
$\operatorname{Sin}\left[-\frac{\pi}{4}\right]=\sin (-1)$
$=-\sin 1$
$\sin 0=0$
$\sin \frac{\pi}{4}=\sin 0$
$=0$
using properties of greatest integer function
$(1) = 1. (0.5) = 0. (0.5) = -1$
Hence, $R(f) = -( \sin 1.0)$

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