Straight line tilt angle the corner between this straight line and the positive direction of an axis abtsiss usually is considered. It is possible to define this corner, proceeding from the equation of a straight line or coordinates of certain points of a straight line.
It is required to you
- Cartesian system of coordinates
Instruction
1. The straight line equation with slope has y appearance = kx+b where k is slope of a straight line. This coefficient also defines a straight line tilt angle. This coefficient is equal to k = to tg?, where? - a corner between the straight line beam located above an axis abtsiss and the positive direction of an axis abtsiss. It is also a straight line tilt angle. It is equal? = arctg(k). If k = 0, then a straight line is parallel to an axis abtsiss or to coincide with it. Then tilt angle? = arctg(0) = 0 that reflects parallelism of a direct axis abtsiss (or their coincidence).
2. If the straight line crosses an axis abtsiss and ordinate axis, then its tilt angle can be determined by coordinates of points of its crossing with these axes. Consider the rectangular triangle formed by these points and the center of coordinates. Let O be the center of coordinates, X - a straight line point of intersection with an axis abtsiss, Y - a straight line point of intersection with ordinate axis. The tangent of angle between a straight line and an axis abtsiss will be equal in a triangle to tg? = OY/OX. Here OY = |y|, OX = |x| where y is coordinate on ordinate axis of a point of intersection of a straight line with ordinate axis, and x - coordinate on ordinate axis of a point of intersection of a straight line with an axis abtsiss.
3. Therefore? = arctg(OY/OX). If the straight line tilt angle sharp, then this tilt angle is also a corner?, If the tilt angle stupid, then it is equal to 180-? = pi-arctg(OY/OX). If the straight line does not pass through the center of coordinates, then it is possible to choose two any points of a straight line with the known coordinates and by analogy to count an inclination tangent of angle. If the equation has y appearance = const, then the tilt angle is equal 0o. If it has an appearance x = const, then the tilt angle is equal 90o.