Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.

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Which properties characterize $\sin, \cos$?

I know a few properties of $\sin$ and $\cos$, for example: $\sin^2+\cos^2=1$ $\sin (a+b) = \sin a\cos b+\cos a\sin b$. $\cos (a+b) = \cos a\cos b-\sin a\sin b$. $\sin (x+\delta) = \sin x$ for some ...