Tangent

The line meeting the another line at the common point is called tangents. The trigonometric function of an acute angle in an right angled triangle that is the ratio of the length of the opposite side,and the ratio of the length of the adjacent side. A straight line or plane that touches a curved surface at a point but it does not intersect at that point.

Defining Properties of Tangent

Following are the Properties of Tangent:

1. Tangent in terms of sine and cosine:

Since the two triangles ADE and ABC are similar, then

ED / AE = CB / AC.

2. Tangents and right triangles:

Just as the sine and cosine can be found as ratios of sides of the right triangles, so the tangent will use three relations . First is tan A=sin A / cos A. Second is sinA=a/c. Third is cos A=b/c. Dividing a/c by b/c and canceling the cA=a/b. That means is that appear, we conclude that tan the tangent is the opposite divided by the adjacent .

3. A tangent touches a circle exactly one place :

Since a tangent touches the circle at exactly one point, and that point must be perpendicular to a radius.

4. The tangent intersects the circle radius at a 90° angle

It is only when the line is tangent to the circle that the radius will touch that line exactly one point and at this point the 'tangent' must intersect with radius at a 90° angle.