Mathematics

The key is recognizing that odd functions have rotational symmetry of 180° around the origin. To show $\sin x$ has this property, you need to check whether $f(-x) = -f(x)$ — that is, whether flipping the input's sign also flips the output's sign. If that relationship holds, then every point $(a, b)$ on the curve has a "mirror partner" at $(-a, -b)$, which is exactly what origin symmetry means.

The key is recognizing that odd functions have rotational symmetry of 180° around the origin. To show $\sin x$ has this property, you need to check whether $f(-x) = -f(x)$ — that is, whether flipping the input's sign also flips the output's sign. If that relationship holds, then every point $(a, b)$ on the curve has a "mirror partner" at $(-a, -b)$, which is exactly what origin symmetry means.