First slide

Functions (XII)

Question

The fundamental period of the function $f (x) = 4 \cos^{4} (\frac{x - π}{4 π^{2}}) - 2 \cos (\frac{x - π}{2 π^{2}})$ is equal to

Moderate

A

$π^{3}$
B

$4 π^{3}$
C

$3 π^{3}$
D

$2 π^{3}$

Solution

$f (x) = {(1 + \cos (\frac{x - π}{2 π^{2}}))}^{2} - 2 \cos (\frac{x - π}{2 π^{2}})$
$= 1 + \cos^{2} (\frac{x - π}{2 π^{2}})$
Period of $f (x) = \frac{π}{\frac{1}{2 π^{2}}} = 2 π^{3}$

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