Taylor polynomial approximations to a sine curve

This demonstration plots the graph of \(y = \sin(x)\) along with an approximating Taylor polynomial. If n is the requested degree of the Taylor polynomial, and n is odd, then the approximating polynomial is \[ P(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots + (-1)^{\frac{n-1}{2}}\frac{x^n}{n!} \]

Degree of Taylor polynomial:

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