How many ways are there to define sine and cosine? Sometimes there are many ways to define a mathematical concept, for example the natural base logarithm. How about sine and cosine?
Thanks.

(This is by no means a comprehensive list.)
Right-triangle definition: the sine (cosine) of an acute angle is the ratio of the lengths of the leg opposite (adjacent to) the given angle to the hypotenuse of the triangle.
Bizarre Geometric Definition: the cosine of an angle in a triangle is $\frac{a^2+b^2-c^2}{2ab}$, where $a$ and $b$ are the lengths of the sides adjacent to the angle and $c$ is the length of the side opposite the angle; the sine of an acute angle is the cosine of its complement; the sine of an obtuse angle is the cosine of its supplement's complement. (edit: this one might be even worse than I'd originally thought as a definition, so perhaps just ignore it.)
Rotation-transformation definition: the sine (cosine) of a magnitude of rotation is the vertical (horizontal) coordinate of the image of the point (1,0) under a rotation of the given magnitude centered at the origin.
Unit circle definition: the sine (cosine) of a directed angle with vertex at the origin and initial ray on the positive x-axis is the y-coordinate (x-coordinate) of the point of intersection of the terminal ray of the angle with the unit circle centered at the origin.
Power series definition:
$$\begin{align}
\sin x&=\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)!}x^{2n+1}=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\cdots
\\\\
\cos x&=\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n)!}x^{2n}=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots
\end{align}$$
Exponential definition:
$$\sin x=\frac{e^{ix}-e^{-ix}}{2i};\quad\quad\cos x=\frac{e^{ix}+e^{-ix}}{2}$$
