The range of f(x) = cos[x] for -frac{pi}{4}

Question

(C) Given the interval $-\frac{\pi}{4} < x < \frac{\pi}{4}$.Since $\pi \approx 3.14$,we have $-\frac{3.14}{4} < x < \frac{3.14}{4}$,which means $-0.78

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$\{\cos 1, 1\}$

Vedclass · Answer

(C) Given the interval $-\frac{\pi}{4} Since $\pi \approx 3.14$,we have $-\frac{3.14}{4} The greatest integer function $[x]$ takes values based on the range of $x$:For $-0.785 For $0 \le x Thus,the possible values for $[x]$ are $\{-1, 0\}$.Now,substitute these values into $f(x) = \cos[x]$:If $[x] = -1$,$f(x) = \cos(-1) = \cos 1$.If $[x] = 0$,$f(x) = \cos 0 = 1$.Therefore,the range of the function is $\{\cos 1, 1\}$.

The range of $f(x) = \cos[x]$ for $-\frac{\pi}{4} < x < \frac{\pi}{4}$ (where $[.]$ represents the greatest integer function less than or equal to $x$) is

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