How can one tell the period of

monkeyman130yb

monkeyman130yb

Answered question

2022-03-24

How can one tell the period of sin(x32) ? Is it (2π)23?

Answer & Explanation

pastuh7vka

pastuh7vka

Beginner2022-03-25Added 13 answers

The solutions of
sin((x+T)32)=sin(x32)
are
(x+T)32=x32+2mπ
and from there,
T=(x32+2mπ)23x
which proves that there is no constant T that works.
(The same computation with sin(x) gives T=(x+2mπ)x
Regan Gallegos

Regan Gallegos

Beginner2022-03-26Added 9 answers

Leaving aside the fact that the function is only defined for x0, you can easily see that
f(x)=32xcos(x32)
If T>0 is a period, we should have f(T)=f(0)=0 and also f(T)=f(0)=0. Then we have
sin(T32)=cos(T32)=0
which is a contradiction.

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