can someone please explain why the graph of $\sin (x) ,0\leq x\leq 2\pi$ is the same graph as $\sin (2x), 0\leq 2x\leq 4\pi$?
I don't understand why they are the same. If I let $\alpha=2x$, then the second equation becomes $\sin (\alpha), 0\leq \alpha \leq 4\pi$ looks different from the first one?
Hint: Multiply all three parts of the inequality by $\alpha=2$. How does it relate to the argument of $\sin$?