So given a simple pendulum, which makes an angle of 0 with the vertical axis in it's resting position.Now the pendulum is moved to a side by an angle $\theta$ with the vertical axis. The components of the vector $mg$ acting on the pendulum are given as: $$F_x = mg \sin \theta$$ $$F_y = mg \cos\theta$$ My question is that given the way the components seem to shift by an angle $\theta$ when the pendulum was shifted, like before moving the pendulum to the side the component would have been exactly parallel to x and y axis respectively but after moving the pendulum the component also change by an angle which may or may not be $\theta$, is the entire coordinate system shifting by this angle $\theta$ or some other angle for the vector $mg$?
Or just let me know what I'm doing wrong here? Or like my understanding about which part is flawed? Would really appreciate any help.