Question

The maximum value of $y=\sin x$, $0\le x\le 2\mathrm{\pi }$, is _______ and occurs at$x=\_\_\_\_\_\_$.

Short answer

The fill ups are:

(a) $\frac{\mathrm{\pi }}{2}$

(b) $1$.

Step-by-step solution

Step 1. Given Information.

The maximum value of $y=\sin x,0\le x\le 2\mathrm{\pi }$ is ______ and occurs at$x=\_\_\_\_\_\_$.

Step 2. Fill up.

The maximum value of $y=\sin x,0\le x\le 2\mathrm{\pi }$, isrole="math" localid="1646998184747" $\frac{\mathbf{\pi }}{\mathbf{2}}$ and occurs atrole="math" localid="1646998217961" $\mathit{x}\mathbf{=}\mathbf{1}$.