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.