To check your understanding of § {Power Series}, you should complete the following activity. A discussion of some of the most important observations you may make is contained in § { %* Wrap-Up: Finding Power Series Coefficients}.

1. Find the first five nonzero coefficients for $\sin(\theta)$ expanded around the origin.
2. Write out a series approximation, correct to fourth order, for $\sin(\theta)$ expanded around the origin. $$\sin(\theta) = \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad $$
3. Find the first four nonzero coefficients for $\sin(\theta)$ expanded around $\theta_0={\pi\over 6}$.
4. Write out a series approximation, correct to fourth order, for $\sin(\theta)$ expanded around $\theta_0={\pi\over 6}$. $$\sin(\theta) = \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad $$