Usually understand slope of tangent direct any function as an inclination tangent of angle. However also the ability to find a tangent of angle of an inclination of a usual straight line, for example, one of the parties of a triangle in relation to another can be necessary for you. Having defined that you should find, act with one of the following ways.
Instruction
1. If you need to count a straight line tilt angle to abscissa axis, and you do not know the straight line equation, lower from any point of this straight line (except a point of intersection with an axis) a perpendicular on an axis. Then measure legs of the received rectangular triangle and find the relation of an adjacent leg to opposite. The received number will be equal to an inclination tangent of angle. It is convenient to use this method not only for studying a tilt angle of a straight line, but also for measurement of any corners, both on the drawing, and in life (for example, a corner of a slope of a roof).
2. If you know the straight line equation, and you need to find a tangent of angle of an inclination of this straight line to abscissa axis, express at through x. As a result you receive expression of type at =kkh +b. Pay attention to k coefficient - it is and there is an inclination tangent of angle between the positive direction of an axis oh and the straight line beam located it is necessary this axis. If k=0, then a tangent is also equal to zero, that is the straight line is parallel or coincides with abscissa axis.
3. If you were given difficult function, for example, square, and you need to find a tangent inclination tangent of angle to this function, or, in a different way, slope, calculate a derivative. Then calculate value of a derivative in the set point to which the tangent will be carried out. The received number also is a tangent inclination tangent of angle. For example, you were given function at = х^2+3х, having counted its derivative, you receive expression at '=2kh +3. To find slope in a point x =3, substitute this value in the equation. As a result of simple calculations it is easily possible to receive at =2*3+3=9, it also is a required tangent.
4. To find a tangent of angle of an inclination of one of the parties of a triangle to another, arrive as follows. Find a sine (sin) of this corner and divide it into a cosine (cos), as a result you receive a tangent of this corner.