Taylor Series Approximation to Cosine

If a function has a Taylor series that is convergent to the function, it is customary to expect that partial sums with more terms provide a better approximation than those with fewer terms. As the example of y = cos(x) shows, this statement must be qualified.

As of 2018, Java plugins are not supported by any browsers (find out more). This Wolfram Demonstration, Taylor Polynomials, shows an item of the same or similar topic, but is different from the original Java applet, named 'RPolynomialTest'. The originally given instructions may no longer correspond precisely.

Minimum and maximum values on the axes that define the view frame are clickable and also respond to the cursor being dragged in their vicinity. To increase a number, click or drag the cursor a little to the right of the central line of the number. To decrease it, click or drag to the left from the central line.

For x large in absolute value, higher degree polynomials provide worse approximation than lower degree polynomials. For such x, the best approximation is given by the constant term y = 1.


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