Real solutions in the interval [0,π]

[robust dagger]

The total number of real solutions of the equation sin(cos(2πx))=0 in the interval [0,π] is ?

Solution: 6, but can't really figure it out

[dapper iris]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations

[robust dagger]

Real solutions in the interval [0,π]

[crisp quartz]

Because $\cos(2\pi x)$ is bounded between $-1$ and $1$, the only possibility is that $\cos(2\pi x)=0$ \ \ $\implies 2\pi x=\frac{\pi}{2}+\pi n \implies x=\frac{1}{4}+\frac{1}{2}n$, where $n$ is an integer. \ \ The required solutions are $1/4, 3/4, 5/4, 7/4, 9/4, 11/4$.

[pine venture]

civil_service_pigeon

[robust dagger]

but why does it goes only to 11/4?

[crisp quartz]

Because the upper bound is pi

[robust dagger]

Oh I get it now thank you!

+close