Polynomial Approximations  Using calculus, it can be shown that the sine and cosine functi...

Polynomial Approximations  Using calculus, it can be shown that the sine and cosine functions can be approximated by the polynomials

and

where x is in radians.

(a) Use a graphing utility to graph the sine function and its polynomial approximation in the same viewing window. How do the graphs compare?

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(b) Use the graphing utility to graph the cosine function and its polynomial approximation in the same viewing window. How do the graphs compare?

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(c) Study the patterns in the polynomial approximations of the sine and cosine functions and predict the next term in each. Then repeat parts (a) and (b). How did the accuracy of the approximations change when an additional term was added?