Question

If the amplitude of \(y={1\over k}\cos(k^2\theta)\) is 2, then what must be the period?

Answer 1

For some general cosine function \(f(x)=a\cos\big(b(x-c)\big)+d\), the period of \(f(x)\) is \(\dfrac{2\pi}{b}\) and the amplitude is \(a\).

The amplitude is \(\dfrac{1}{k}=2\), so \(k=\dfrac{1}{2}\).

The period would be \(\dfrac{2\pi}{k^2}=\cdots\)

Answer 2

so that would make it \[2\pi\over .25\]which would be \(8\pi\), yes? :D

Answer 3

Yep

Answer 4

thanks!!

Answer 5

You're welcome!