I want to show that a sequence $\sin(n\pi x)$ where $x$ is in $[0,1]$ is decreasing? is there any test I can apply and if there is no test can somebody please tell me how to show it?
since I think that i am doing wrong. what I did:
$\sin((n+1)\pi x)=\sin(n\pi x+\pi x)=\sin(n\pi x)\cos(n\pi)+\sin(n\pi)\cos(n\pi x)<\sin(n\pi x)$ but why???