1. **State the problem:** We need to analyze the function $f(x) = \sin(x + \pi)$ to find its periodic time (period) and points of intersection with the horizontal axis and the edges. 2. **Recall the formula and properties:** The sine function $\sin(x)$ has a period of $2\pi$, meaning it repeats every $2\pi$ units. 3. **Period of $f(x)$:** Since $f(x) = \sin(x + \pi)$ is a horizontal shift of $\sin x$ by $-\pi$, the period remains the same. $$\text{Period} = 2\pi$$ 4. **Find zeros (points of intersection with the horizontal axis):** Solve for $x$ when $f(x) = 0$: $$\sin(x + \pi) = 0$$ The sine function is zero at integer multiples of $\pi$: $$x + \pi = k\pi, \quad k \in \mathbb{Z}$$ Solve for $x$: $$x = k\pi - \pi = (k - 1)\pi$$ So zeros occur at $x = (k - 1)\pi$ for all integers $k$. 5. **Points of intersection with edges:** If edges refer to boundaries of one period, say from $0$ to $2\pi$, evaluate $f(x)$ at these points: At $x=0$: $$f(0) = \sin(0 + \pi) = \sin(\pi) = 0$$ At $x=2\pi$: $$f(2\pi) = \sin(2\pi + \pi) = \sin(3\pi) = 0$$ Both edges intersect the horizontal axis. **Final answers:** - Period: $2\pi$ - Zeros: $x = (k - 1)\pi$, $k \in \mathbb{Z}$ - Intersections at edges $x=0$ and $x=2\pi$ are zero.