The series

converges to sin x for all x.

a. Find the first six terms of a series for cos x. For what values of x should the series converge?

b. By replacing x by 2x in the series for sin x, find a series that converges to sin 2x for all x.

c. Using the result in part (a) and series multiplication, calculate the first six terms of a series for 2 sin x cos x. Compare your answer with the answer in part (b).

Transcribed Image Text:

sin x = x - + + 11! +