Is it possible to trigonometrically understand why $\cos(x)$ is even and $\sin(x)$ is odd?
2026-02-23 18:45:37.1771872337
Is it possible to trigonometrically understand why $\cos(x)$ is even and $\sin(x)$ is odd?
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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).