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Taylor series for sin(x) and cos(x), Single Variable Calculus
Let's compute the Taylor series (or Maclaurin series) for f(x)=sin(x) and g(x)=cos(x) centered at x=0. We compute the Maclaurin series for sin(x) using the definition of Taylor coefficients: we start with the function đť‘“(đť‘Ą)=sin(đť‘Ą) and its derivatives, evaluating them at đť‘Ą=0, until we observe a cyclic pattern in the derivatives. We ...
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