First slide

Functions (XII)

Question

The value of $n \in z$ for which the function $f (x) = \frac{\sin n x}{\sin (x / n)}$ has $4 π$ as its period is

Moderate

A

2
B

3
C

4
D

5

Solution

$f (x + 4 π) = f (x)$
If $\frac{\sin n (x + 4 π)}{\sin \frac{x + 4 π}{n}} = \frac{\sin n x}{\sin \frac{x}{n}}$
which holds if $n = 2 .$

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