Question:

<div class="solution"><p><strong>Step 1:</strong> $3\pi\approx 9.42$. So $3\pi-10\approx -0.58\in[-\pi/2,\pi/2]$.</p><p><strong>Step 2:</strong> $\sin(3\pi-10)=\sin(\pi-(10-2\pi))=\sin(10-2\pi)=\sin 10$. Wait -- simpler: $\sin(3\pi-\theta)=\sin\theta$, so $\sin(3\pi-10)=\sin 10$. And $3\pi-10\in[-\pi/2,\pi/2]$. ✓</p><p><strong>Answer: (3) $3\pi-10$</strong></p><div class="trap-box"><strong>Trap:</strong> Taking sin⁻^1(sin 10)=10 -- wrong, 10\notin[-\pi/2,\pi/2].<div class="key-concept"><strong>Key Concept:</strong> Use multiples of \pi to pull angle into principal range [-\pi/2,\pi/2]