I am trying to find a bound for

metalskaashw

metalskaashw

Answered question

2022-03-30

I am trying to find a bound for |cos(2n+1)θ| by something of the form c(n)|cosθ| . I am suspecting that we can bound it by (2n+1)|cosθ| but I'm not sure how to show that this is true

Answer & Explanation

Denise Daniel

Denise Daniel

Beginner2022-03-31Added 8 answers

Use . Then
cos(2n+1)tcost=e(2n+1)it+e(2n+1)iteit+eit=e2nite2(n1)t+e2(n2)it+e2nit
As each of these exponentials is bounded by 1 is absolute value, you get
|cos(2n+1)t|(2n+1)|cost|
This is the best possible; take t close to π2, then e2it is close to -1 etc.

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