What is Cosine and sine?

For every real $t$, the cosine and sine of $t$ are the coordinates of the point $M(t)$ of the unit circle:

Let $\mathcal{C}$ be the circle of radius 1 centered at the origin of an orthonormal coordinate system. To each real $t$, associate the point $M(t)$ obtained by winding a length $\abs{t}$ along $\mathcal{C}$ from the point $I(1,0)$, counterclockwise if $t \geq 0$ and clockwise otherwise. Then $\cos t$ and $\sin t$ are the coordinates of $M(t)$: