ANSWER
The period is
[tex] \frac{\pi}{8} [/tex]
EXPLANATION
The given function completes four cycles on the interval
[tex]
[ - \frac{\pi}{4} , \frac{\pi}{4} ][/tex]
Therefore the period is
[tex] = \frac{ \frac{\pi}{4} - \frac{\pi}{4} }{4} [/tex]
Simplify the numerator:
[tex] = \frac{ \frac{\pi}{2}}{4} [/tex]
Simplify further to get:
[tex]= \frac{\pi}{8} [/tex]
