Taylor Polynomial Exploration

Consider the functions sin(x) and cos(x) and their Taylor Polynomials. Move sliders n and c to change the degree and center respectively. Move n to 3 and c to 0. Look at the polynomials that are created. Using the power rule, is the derivative of the series for sine equal to the series for cosine? How about integration? Is the integral of the series for cosine equal to the series for sine? Change sliders n and c to compare different series and their derivatives and integrals.