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

Answer:

$\frac{3\pi}{2}$

Explanation:

Step1: Set up the equation

$- \sin x=-1$

Step2: Solve for $\sin x$

$\sin x = 1$

Step3: Find $x$ in the given range

We know that $\sin x = 1$ when $x=\frac{\pi}{2}+ 2k\pi,k\in\mathbb{Z}$. In the range $0 < x<2\pi$, when $k = 1$, $x=\frac{3\pi}{2}$.