Let $C=\{x: \sin 4x=1/2,\ x\in(-9\pi,3\pi)\}$. What is the cardinality of $C$?

Explanation

$-9\pi < x < 3\pi$ Multiplying by $4$ $-36\pi < 4x < 12\pi$ In each interval of length $2\pi$, equation $\sin\theta=1/2$ has $2$ solutions Number of intervals $=(48\pi)/(2\pi)=24$ Total solutions $=24 \times 2 = 48$