If \( \sin \theta = -1 \), then \( \theta = 270^\circ \)
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- So, \( \sin \theta = \frac{1}{2} \) or \( \sin \theta = -1 \).
- Solve for \( \theta \in [0^\circ, 360^\circ] \):
- If \( \sin \theta = \frac{1}{2} \), then \( \theta = 30^\circ, 150^\circ \)
- Check each solution in the original equation:
- \( \theta = 30^\circ \): \( \cos 60^\circ = \frac{1}{2},\ \sin 30^\circ = \frac{1}{2} \) → valid
- \( \theta = 150^\circ \): \( \cos 300^\circ = \frac{1}{2},\ \sin 150^\circ = \frac{1}{2} \) → valid
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