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)