$8$ Section $11\mathrm{.}10$

Find the Maclaurin series for $cosx.$ Use formula $7$ on page $796$ which requires you to compute and evaluate the first four derivatives of $cosx$ at $x=0.$ Express your final answer in the form

$a_0+a_2{x}^2+a_4{x}^4+$cdots$={\displaystyle \underset{n=0}{\overset{}{}}}{a}_{2n}{x}^{2n}$

Now use differentiation $(sinx=-co{s}^{\text{'}}x)$ to find the Maclaurin series for $sinx$ from the Maclaurin series for $cosx.$