First slide

Functions (XII)

Question

The period of the function $f (x) = \sin \frac{π}{4} [x] + \cos \frac{π}{2} x + \cot \frac{π}{3} [x]$

Moderate

A

24
B

20
C

43
D

21

Solution

$\sin \frac{π}{4} (8 + [x]) = \sin \frac{π}{4} [x],$ so its period is 8.
The period of $\cos \frac{π}{2} x$ is 4 and $\cot \frac{π}{3} [3 + [x]) = \cot \frac{π}{3} [x]$ is 3.

Hence period of $f (x)$ is $L . c . m (8, 4, 3) = 24.$

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