Maclurin Series. (Approximation) Given that $y=\ln \cos x$, show that the first non-zero terms of Maclurin's series for $y=-\frac{x^2}{2}-\frac{x^4}{12}$. Use this series to find the approximation in terms of $\pi$ for $\ln 2$.
My question is how to determine value of $x$ which is suitable?

$$\cos\left(\dfrac{\pi}{3}\right)=\dfrac{1}{2}$$
$$\ln\cos(\pi/3)=\ln(1/2)=\ln(1)-\ln(2)=-\ln(2)$$
