[tex]\displaystyle \sf f(x) = a+b\cdot sen\left(m\cdot x + n\right) \\\\ \text{per\'iodo }= \frac{2\pi }{|m|} } \\\\\\ temos: \\\\ m(x) =5+sen\left(\frac{\pi}{4}\right) \\\\ \text{per\'iodo }=\frac{2\pi}{\displaystyle \left|\frac{1}{4}\right|} \\\\\\ \text{per\'iodo} = 2\pi \cdot \frac{4}{1} \\\\ \Large\boxed{\sf \ \text{per\'iodo} = 8\pi \ }\checkmark[/tex]

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