Projection of Simple Pendulum Motion

Angular position $\theta$ of simple pendulum, with bob mass $m$ and arm length $L$, relates to projection along horizontal direction

$$\tag{1} x = x_c + L \sin\theta $$

and vertical direction

$$\tag{2} y = y_c - L \cos\theta, $$

with positive direction of $\theta$ is in counter clockwise direction and $(x_c, y_c)$ is pivot position.