To rewrite the function \( f(x) = \cos(2x + \pi) \) as a sine function, we can use the identity \( \cos(\theta) = -\sin\left(\theta + \frac{\pi}{2}\right) \).
Thus, we have:
\[ f(x) = \cos(2x + \pi) = -\sin\left(2x + \pi + \frac{\pi}{2}\right) = -\sin\left(2x + \frac{3\pi}{2}\right) \]
In simpler terms, the function \( f(x) = \cos(2x + \pi) \) can be expressed as \( f(x) = -\sin\left(2x + \frac{3\pi}{2}\right) \). This demonstrates the relationship between cosine and sine functions through phase shifts.
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