The tangent of an angle is defined as the ratio between the side opposite the angle
and the adjacent leg. As you can see in this magic pitcure, in a right
triangle with a hypotenuse of 1, these two sides have lengths of the
sine of the angle and the cosine of the angle. This shows that the
tangent of any angle is equal to the sine of the same angle divided
by the cosine of the angle. The side which is labeled as the tangent
forms a right triangle in which the near leg has a length of 1. Since the
tangent is defined as the far leg divided by the near one and the near
leg has a length of 1, this division again can be left out and the
tangent can be read straight off the far leg.
Move your mouse over the example to see the range of these different functions. For example, the sine will never get bigger than one, while the tangent can get infinitly big.