**Sine, cosine, and
tangent**

The **sine** of
an angle is the ratio of the length of the opposite side to the length of the
hypotenuse. In our case

Note that this
ratio does not depend on size of the particular right triangle chosen, as long
as it contains the angle *A*, since all such triangles are similar.

The **cosine**
of an angle is the ratio of the length of the adjacent side to the length of
the hypotenuse. In our case

The **tangent**
of an angle is the ratio of the length of the opposite side to the length of
the adjacent side (called so because it can be represented as a line segment
tangent to the circle)[1]. In our case

u = V*sin(rad*dir)

v = V*cos(rad*dir)