Solution

In a secure communication system, the phase shift $\theta$ (in radians) of an encrypted signal is modeled by the nonlinear function $f(\theta) = \sin \theta - 0.5$. For proper synchronization of the encrypted signal, the phase shift must satisfy $f(\theta) = 0$. Use the Newton–Raphson Method with initial guess $\theta_0 = 0.5$ to determine the required phase shift $\theta$, correct to three decimal places.