The bevel and slope of a straight line, what is the inclination angle of a straight line

Yes. If the line intersects the x-axis, the angle experienced by the first time that the x-axis rotates counterclockwise around the intersection point is called the inclination angle of the line. If the line is parallel or coincident with the x-axis, the tilt angle is 0. The tangent of the angle of inclination is the slope.

Only help with question 10, which is solved as follows:

10.Solution: (1) Straight line l1: (y-1) (x+2)=(0+2) (5-1),y-1=(x+2) 2,y=x 2+2;

Straight line l2: (y-1) (x+2)=(3+2) (4-1),y-1=5(x+2) 3,y=5x 3+13 3;

Straight line l3: (y-3) (x-4) = (0-3) (5-4), y-3 = -3 (x-4), y = -3x+15

Because there is no k=-1 k, this triangle is not a right triangle.

2) Straight line l1: (y+7) (x-10)=(9+7) (-2-10),y+7=-4(x-10) 3,y=-4x 3+19 3;

Straight line l2: (y+7) (x-10)=(-5+7) (12-10), y+7=x-10;

Straight line l3: (y-9) (x+2)=(-5-9) (12+2), y-9=-(x+2), y=-x+7

Because K2 = 1 for the straight line L2 and K3 for the straight line L3 = -1=-1 K2, this triangle is a right triangle.

The angle of inclination of a straight line is

1. Definition: The angle between the forward direction of the x-axis and the upward direction of the straight line is called the inclination angle of the straight line When the straight line is parallel or coincides with the x-axis, its inclination angle is specified as 0°.

2. The range of the inclination angle is [0, ).

For example, if the straight line l passes through the origin, its inclination angle is a, and the straight line l is rotated 45° in the counterclockwise direction around the coordinate origin to obtain the straight line l1, then the inclination angle of the straight line l1 is ( ).

a．a+45°。

b．a－135°。

c．135°－a。

d A+45° when 0° A 180°, and A 135° when 135° A 180°.

In the planar Cartesian coordinate system, for a straight line that intersects the x-axis, if the smallest positive angle of rotation of the x-axis around the intersection point in a counterclockwise direction to coincide with the line is recorded as a, then a is called the inclination angle of the line.

Stipulation: When the line and the x-axis are parallel or coincide, the inclination angle of the straight line is a, so the range of the inclination angle is 0<=a<=180.

StraightTilt angleRelation to slope: k=tan.

k is the slope and is the angle of inclination. The slope is equal to the tangent of the tilt angle.

For example, a simple proportional function.

y=x, the slope is 1, the tilt angle is 45 degrees, and tan45°=1.

Introduction to Slope and Tilt Angle:

Slope k=tan ( angle of inclination).

So we can only say the absolute value of the slope of the blindness.

The larger it is, the closer the represented straight line is to the y-axis.

And because tan180 degrees 0.

So in fact, when the tilt angle is close to 180 degrees, the absolute pre-material value of the slope is close to 0.

Definition of slope:

The slope, also known as the "angular coefficient", represents the planar Cartesian coordinate system.

, which represents the degree to which a line is tilted to the abscissa axis.

The tangent tg of the angle of inclination of the line to the x-axis tg is called the "slope" of the line and is denoted as k, k=tg. Specifies the slope of a straight line parallel to the x-axis.

is zero, and the slope of the line parallel to the y-axis does not exist. For a straight line passing through two known points (x1,y1) and (x2,y2), if x1≠x2, the slope of the line is k=(y1-y2) (x1-x2). i.e. k=tan (y1-y2) (x1-x2).

Straight lineTilt angleThe value range is 0 degrees to 180 degrees (0 degrees can be taken, but not 180 degrees); The slope is a representation of a straight line (or curveTangentsAbout (horizontal).AxesThe amount of inclination. It is usually expressed as the tangent of the angle between the straight line (or the tangent of a curve) and the (horizontal) axis, or the ratio of the difference between the ordinates of two points to the difference between the abscissa of the abscissa.

The tangent of a straight line to the positive angle of the abscissa axis reflects the inclination of Zhengchang's straight line to the horizontal plane. A straight line and a plane Cartesian coordinate system.

The tangent of the angle in the direction of the positive semi-axis of the abscissa axis.

That is, the slope of the line with respect to the coordinate system.

The tangent of the angle of inclination of the x-axis of the straight line is called the "slope" of the line and is denoted as k, and the formula is k=tan. Sepure specifies the slope of a straight line parallel to the x-axis.

is zero, and the slope of the line parallel to the y-axis does not exist. For a straight line passing through two known points (x1,y1) and (x2,y2), if x1≠x2, the slope of the line is k=(y1-y2) (x1-x2).

When the slope of the straight line l exists, the oblique truncated y=kx+b. When x=0, y=b.

General equation for straight lines: ax + by + c = 0 (a≠0 &&b≠0) [applies to all straight lines].

Slope refers to the tangent value of the angle between a straight line and the direction of the transverse axis and semi-axis of the plane Cartesian coordinate system, that is, the slope of the straight line relative to the coordinate system.

The cross-section is the distance between the point (a,0) where a straight line intersects the transverse axis from the origin, and the general formula is: a = c a.

The longitudinal intercept is the distance between the point (0,b) and the origin of a straight line intersecting the longitudinal axis, and the general formula is: b = c b.

Example: A straight line is known to have an equation of 2x - y + 3 = 0

1. Cross-section(-c a): 3 2 = ;

2. Longitudinal intercept (-c b): 3 -1 = 3;

3. Slope (-a b): 2 -1 = 2.

Tilt angleThe value range is 0 degrees to 180 degrees (you can take 0 degrees, you can't take 180 degrees); The slope is a representation of a straight line (or curveTangentsAbout (horizontal).AxesThe amount of inclination.

It has an infinite number of axes of symmetry.

One of them is itself, and all the straight lines (there are innumerable) axes of symmetry perpendicular to it. There is only one straight line at the two points that do not coincide on the plane, that is, a straight line is determined if the two points do not coincide. On a spherical surface, crossing two points can make an infinite number of similar straight lines.

About the content. Let the normal vector of the plane e.

is the direction vector of the c line m and n.

For a and b, the normal vectors of the plane ax+by+cz+d=0 are (a, b, c); The direction vector of the straight line x=kz+b, y=lz+a is (k,l,1).

Then the angle formed by the straight line: the angle formed by mn is a.

cosa=cos=|a*b|/|a||b|

The angle formed by the straight line and the plane: Let b be the angle formed by the auspicious beams of m and e, then b = 2. sinb=|cos|=|a*c|/|a||c|

The angle formed by two straight lines in a plane is k(l1)=k1,k(l2)=k2(k1k2≠-1), tan1,l2>=(k1-k2) (1+k1k2).

The value range of the straight line inclination angle is 0 degrees to 180 degrees (0 degrees can be taken, but 180 degrees cannot be taken).；Slope is the amount that represents how much a straight line (or tangent of a curve) is tilted with respect to the (horizontal) axis. It is usually expressed as the tangent of the angle between the straight line (the tangent of the Naku or the curve) and the (horizontal) axis, or the ratio of the difference between the ordinates of two points to the difference between the abscissa of the abscissa.

The tangent of a straight line to the positive angle of the abscissa axis reflects the inclination of the line to the horizontal plane. The tangent of the angle between a straight line and the abscissa axis of a plane Cartesian coordinate system, that is, the slope of the straight line relative to the coordinate system.

NEED NOTICE:

The tangent of the angle of inclination of the line to the x-axis tan is called the "slope" of the line and is denoted as k, and the formula is k=tan. It is specified that the slope of a straight line parallel to the x-axis is zero, and the slope of a straight line parallel to the y-axis does not exist. For a straight line passing through two known points (x1,y1) and (x2,y2), if x1≠x2, the slope of the line is k=(y1-y2) (x1-x2).

When the slope of the straight line l exists, the oblique truncated y=kx+b. When x=0, y=b.

The range of the inclination angle of a straight line is: Sozen [0, )

If the limb circle = 90°, the slope of the straight line does not exist;

If ≠90°, then the slope of the line is k=tan

The inclination angle and slope of the straight line are as follows:

The value range of the inclination angle is 0 degrees to 180 degrees (0 degrees can be taken, but 180 degrees cannot be taken); Slope is the amount that represents how much a straight line (or tangent of a curve) is tilted with respect to the (horizontal) axis.

It has an infinite number of axes of symmetry, one of which is itself, and all the straight lines (with an infinite number of axes) perpendicular to it. If there is a leak in the two points that do not coincide on the plane and there is only one straight line, that is, the two points that do not coincide determine a straight line. On a spherical surface, a two-point return can make an infinite number of similar straight lines.

About the content. Let the normal vector of the plane e be c, the direction vector of the straight line m and n be a, b

The normal vector of the plane ax+by+cz+d=0 is (a,b,c); The direction vector of the straight line x=kz+b, y=lz+a is (k,l,1).

Then the angle formed by the straight line: the angle formed by mn is a. <>

cosa=cos=|a*b|/|a||b|

Angles of straight lines and planes: Let b be the angles of m and e, then b = 2. sinb=|cos|=|a*c|/|a||c|

The angle formed by two straight lines in the plane: K(L1)=K1,K(L2)=K2(K1K2≠-1), Tan1,L2>=(K1-K2) (1+K1K2).