The tangent of an angle is the trigonometric ratio between the adjacent side and the opposite side of a right triangle containing that angle. In this-sub-topic we will learn more about the tangent of an angle. We will learn about the values of the tangent of important angles and we will solve some practice problems.

The tangent of an angle can be defined using a right triangle. The tangent is equal to the length of the side opposite the angle divided by the length of the adjacent side.

In any right triangle, the tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A). It is written simply as “tan”. Using the right triangle ABC which is a right angle at C, shown in figure 8, the tangent of an angle can be defined as follows:

The circle with center (0, 0) and radius 1 unit is called the unit circle.

Let the terminal side of θ intersects the unit circle at point P(x, y). Since

the sine, cosine and tangent function of θ are given as follows: