Question

Elliptic Functions: Find the Maclaurin series for E(k) and estimate E(k) for k=sin(Pie/6)

Answer 1

For the sin(π/6) we want the Maclaurin series for sine which is \[\sum_{n=0}^{\infty}(-1)^{n}x ^{2n+1}/(2n+1)!\]
this simplifies to x-x^3/3!+x^5/5!-x^7/7! ....
for π/6 just replace x with π/6 and you should get the answer. That is if I remember my Maclaurin Series approximation correctly...