Question

Com explicação
Mostre que a função f(x) + 1 + sen(3 π • X/4) é periódica de período p=8/3

Answer 1

$\Large\boxed{\begin{array}{l}\sf Dada\,a\,func_{\!\!,}\tilde ao~f(x)=a+bsen(cx+d)\\\sf o\,per\acute iodo\,de\,f(x)\,\acute e\,p=\dfrac{2\pi}{c}.\\\sf f(x)=1+sen\bigg(\dfrac{3\pi\cdot x}{4}\bigg)\\\\\sf p=\dfrac{2\pi}{\dfrac{3\pi}{4}}\\\\\sf p=2\diagdown\!\!\!\!\pi\cdot\dfrac{4}{3\diagdown\!\!\!\!\pi}\\\\\sf p=\dfrac{8}{3}\end{array}}$