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Consider the Maclaurin series for \(\cos(t)\):$$ \cos(t) = 1 - \frac{t^2}{2!} + \frac{t^4}{4!} - \frac{t^6}{6!} + \dots $$By integrating both sides of this equation from \(0\) to \(x\), find the Maclaurin series for the function \(f(x) = \sin(x)\).
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