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$\cos(-x) = \cos(x)$, which shows that the cosine function is an even function.

The sum-to-product formulae for sine and cosine can be written as $\sin(x) \pm \sin(y) = 2\sin(\frac{x \pm y}{2})\cos(\frac{x \mp y}{2})$ and $\cos(x) + \cos(y) = 2\cos(\frac{x + y}{2})\cos(\frac{x - y}{2})$.

The sine function repeats its values every $2\pi$ radians.

The cosine function repeats its values every $2\pi$ radians.

$\sin(-x) = -\sin(x)$, indicating that the sine function is an odd function.

The amplitude is the maximum value of the sine or cosine function, which is 1.

$\tan(-x) = -\tan(x)$, meaning the tangent function is odd symmetric.