1. **Problem Statement:** Given the sine curve $y = \sin x^\circ$ for $0 \leq x \leq 360$, and knowing that $\sin 30^\circ = \frac{1}{2}$, find: (i) $\sin 150^\circ$ (ii) $\sin 330^\circ$ 2. **Formula and Important Rules:** The sine function has the property that $\sin(180^\circ - \theta) = \sin \theta$ and $\sin(360^\circ - \theta) = -\sin \theta$. 3. **Step-by-step Solution:** (i) Calculate $\sin 150^\circ$: Using the identity: $$\sin 150^\circ = \sin(180^\circ - 30^\circ) = \sin 30^\circ$$ Since $\sin 30^\circ = \frac{1}{2}$, then: $$\sin 150^\circ = \frac{1}{2}$$ (ii) Calculate $\sin 330^\circ$: Using the identity: $$\sin 330^\circ = \sin(360^\circ - 30^\circ) = -\sin 30^\circ$$ Since $\sin 30^\circ = \frac{1}{2}$, then: $$\sin 330^\circ = -\frac{1}{2}$$ 4. **Final Answers:** (i) $\sin 150^\circ = \frac{1}{2}$ (ii) $\sin 330^\circ = -\frac{1}{2}$