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Question: Compute $ (\cos \theta + i \sin \theta)^5 $ using De Moivre’s theorem.
Solution: By De Moivre’s theorem, $ (\cos \theta + i \sin \theta)^n = \cos(n\theta) + i \sin(n\theta) $. Applying $ n = 5 $, the result is $ \cos(5\theta) + i \sin(5\theta) $. \boxed{\cos(5\theta) + i \sin(5\theta)}
Question: Find the range of $ f(x) = \frac{2\sin x + 1}{\sin x - 3} $ for $ x $ where the denominator is nonzero.

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