## The Tangent Function

The tangent function is one of the three important trigonometric function. For an angle in a right angled triangle is the the ratio of the side opposite the angle and the side adjacent to the angle.

For right angled trianglesand

We can write

If we draw a straight line through the origin on a set of axes,

we can make a right angles triangle with two sides parallel to the axes as shown below. The line makes an anglewith the– axis.

If the coordinates of the top right hand corner of the triangle arethen the height of the triangle isand the base of the triangle isThenbut by definition this is equal to the gradient of the line so we can write the equation of the line as