Como $$\\begin{array}{*{20}{l}}
\n{h(x + \\frac{{2\\pi }}{\\alpha })}& = &{\\cos \\left[ {\\alpha \\left( {x + \\frac{{2\\pi }}{\\alpha }} \\right)} \\right] + \\operatorname{sen} \\left[ {\\alpha \\left( {x + \\frac{{2\\pi }}{\\alpha }} \\right)} \\right]} \\\\
\n{}& = &{\\cos \\left( {\\alpha x + 2\\pi } \\right) + \\operatorname{sen} \\left( {\\alpha x + 2\\pi } \\right)} \\\\
\n{}& = &{\\cos \\left( {\\alpha x} \\right) + \\operatorname{sen} \\left( {\\alpha x} \\right)} \\\\
\n{}& = &{h(x)}
\n\\end{array}$$
\nent\u00e3o $h(x + \\frac{{2\\pi }}{\\alpha }) = h(x),\\forall x \\in \\mathbb{R}$, com $\\alpha\u00a0 \\ne 0$.<\/p>\n\u00a0Logo, $\\frac{{2\\pi }}{\\alpha }$ \u00e9 per\u00edodo da fun\u00e7\u00e3o $h$.
\n\u00ad<\/p>\n<\/li>\n<\/ol>\n