FunctionPeriod[Sin[16 Pi x/5 - Pi/8], x, Integers]
80
then I ListPlot
the function:
ListPlot[Transpose[{Range[0, 90], Sin[16/5 π Range[0, 90] - π/8]}], Filling -> Axis]
then I test the number:
Union[Simplify[Sin[16/5 π Range[0, 90] - π/8]]]
{-Cos[π/40], Cos[(7 π)/40],Cos[(9 π)/40], -Sin[(3 π)/40], -Sin[π/8]}
so I wonder why Mathematica gives 80 instead of 5?
FunctionPeriod
says it "gives a period p of the function f over the reals such that f(x+p)==f(x)". This is certainly the case here: 80 is "a period" of the function. Nowhere in the docs does it say that it will give the minimum period (in this case 5). $\endgroup$