Mathematics

The key is recognizing that $\sin x = 0$ at the points where the sine curve crosses the horizontal axis—these are the angles where the $y$-coordinate on the unit circle equals zero. Rather than memorizing, think about where on the circle the point lands directly on the $x$-axis: that happens at the "cardinal" positions, spaced evenly around the circle. Within your given interval, you just need to identify which of these special angles fall in $[-\pi, \pi]$.

The key is recognizing that $\sin x = 0$ at the points where the sine curve crosses the horizontal axis—these are the angles where the $y$-coordinate on the unit circle equals zero. Rather than memorizing, think about where on the circle the point lands directly on the $x$-axis: that happens at the "cardinal" positions, spaced evenly around the circle. Within your given interval, you just need to identify which of these special angles fall in $[-\pi, \pi]$.