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 triangles
and
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 angle
with the
– axis.
If the coordinates of the top right hand corner of the triangle are
then the height of the triangle is
and the base of the triangle is
Then
but by definition this is equal to the gradient of the line so we can write the equation of the line as