Sine and Cosine: The Eternal Archetypes

In cal­cu­lus, sym­me­try and anti-sym­me­try man­i­fest as cosine (even) and sine (odd):

• Cosine: $\cos(-x) = \cos(x)$. A wave of sym­me­try, re­flect­ing itself like the number $2$.

• Sine: $\sin(-x) = -\sin(x)$. A wave of anti-sym­me­try, in­vert­ing itself like the number $3$.

To­geth­er, they form the Fouri­er basis, de­com­pos­ing func­tions into sym­met­ric and anti-sym­met­ric parts.