Use Theorem 2.3 to show that g(x) = π + 0.5 sin(x/2) has a unique fixed point on [0, 2π]...

Use Theorem 2.3 to show that g(x) = π + 0.5 sin(x/2) has a unique fixed point on [0, 2π]. Use fixed-point iteration to find an approximation to the fixed point that is accurate to within 10−2. Use Corollary 2.5 to estimate the number of iterations required to achieve 10−2 accuracy, and compare this theoretical estimate to the number actually needed.

Reference: Theorem 2.3