Intuition for reflections/symmetry, shifts, parity, and periodicity of sine and cosine functions at allied angles 0, $π/2$, $π$, $3π/2$, and $2π$

Question

I have proved the table given above, for example, $\cos \left( \dfrac{\pi }{2}-\theta \right) =\sin \theta $ and $\cos \left( \dfrac{\pi }{2}+\theta \right) =-\sin \theta $ using sum/difference identities, but I need intuition (using unit circle/right triangle/graphs, etc.) for understanding and remembering the same. I need Intuition for understanding and remembering the reflections/symmetry, shifts, parity, and periodicity of sine and cosine functions at allied angles 0, $π/2$, $π$, $3π/2$, and $2π$.