if y = -sin x, what x - value corresponds to a y - value of 1 between 0 and 2π?

Explanation:

Step1: Set up the equation

Set $y = 1$ in $y=-\sin x$, so we get $1 = -\sin x$, which can be rewritten as $\sin x=- 1$.

Step2: Find the x - value in the given interval

We know that the sine - function $y = \sin x$ has a value of $-1$ when $x=\frac{3\pi}{2}+2k\pi,k\in\mathbb{Z}$. In the interval $0\lt x\lt2\pi$, when $k = 0$, $x=\frac{3\pi}{2}$.

Answer:

$\frac{3}{2}$