Extend an inverse-cosine piece periodically and solve a threshold

Repeat the inverse-cosine descent and linear ascent every 2 units. On $[-3,4]$, the zeros are $(-3,0),(-1,0),(1,0),(3,0)$, and the peaks are $(-2,\pi/2),(0,\pi/2),(2,\pi/2),(4,\pi/2)$. The joins are continuous and both window endpoints are included. Here $\cos^{-1}$ means inverse cosine, not reciprocal cosine.

On $0\leq x<1$, $\cos^{-1}x=\pi/3$ gives $x=1/2$, and the graph exceeds the level for $0\leq x<1/2$. On $1\leq x<2$, $\frac\pi2x-\frac\pi2=\pi/3$ gives $x=5/3$, and the graph exceeds the level for $5/3<x<2$. Extend by period 2 and join across the included peak at 2: $0\leq x<1/2$ or $5/3<x<5/2$ or $11/3<x\leq4$. The four threshold crossings are excluded because the inequality is strict; 0 and 4 are included because their values are $\pi/2$.