Is it possible to trigonometrically understand why $\cos(x)$ is even and $\sin(x)$ is odd? Is it possible to trigonometrically understand why $\cos(x)$ is even and $\sin(x)$ is odd? ![enter image description here](

Yes, it is: sending $\theta$ to $-\theta$ amounts to flipping the $y$-axis in your drawing, and then the cosine is unaffected since the $x$-axis is fixed, but the sine changes sign (since the $y$-axis is flipped).