Question:

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