Use Example 12 and the approximation sin x x to show that the period T of a pendulum released at an angle has

Use Example 12 and the approximation sin x ≈ x to show that the period T of a pendulum released at an angle θ has the following second-order approximation:

EXAMPLE 12 Elliptic Function Find the Maclaurin series for E(k) and estimate E(k) for k= sin.