Slope ratio size, how to compare slope size

Before your question, let's review exactly three basic concepts (from Compulsory 2 textbooks). 1. The inclination angle of the straight line: when the straight line l intersects with the x-axis, the angle a between the positive direction of the x-axis and the upward direction of the straight line is called the inclination angle of the straight line The range of inclination angles:

0<=a<180 degrees (note, including 0, excluding 180 degrees) 2. The slope of the straight line: the tangent of the inclination angle a of the straight line is called the slope of the straight line k=tana The range of slope: (infinity, 0) [0, +infinity) The range of the inclination angle:

90 degrees, 180 degrees) [0, 90 degrees) (Note that there is no slope at the 90 degree inclination angle) 3. The inclination degree of the slope of the daily slope is expressed by the slope (ratio): Slope (ratio) = elevation Advance = tana = k Slope is the slope Question 1: The slope of the acute angle is greater than the slope of the obtuse angle, right?

To be precise: Is it true that the slope of a straight line with an acute angle of inclination is greater than the slope of a straight line with an obtuse angle? Analysis:

When a belongs to [0, 90 degrees), k1=tana>=0 When b belongs to (90 degrees, 180 degrees), k2=tana<0 k1>k2, which shows that this is true Question 2: The slope can indicate the degree of inclination of a straight line, and the degree of inclination is based on the slope!

There are two cases, bai one: when the straight line is from the bottom left to the right du

When extending upward, the steeper the slope, the larger the slope, the smaller the slope, the smaller the slope, two: when the straight line extends from the left to the right, the larger the slope, the smaller the slope, and the smaller the slope, the greater the slope. The slope is always positive in the first case and negative in the second.

It is important to note that the slope is 0 when the line is parallel to the x-axis, and the slope is absent when the line is perpendicular to the x-axis.

1: When the slope is positive, the closer the line is to the x-axis, the smaller the slope; 2. When the slope is negative, the closer the line is to the x-axis, the greater the slope.

To judge the slope is to judge the magnitude of k. It is to look at the angle between the vertical line of the front wheel and the x-axis. The larger the angle, the greater the slope.

The slope is also the meaning of the tan angle. The image of the tan is monotonically increasing from 0 to 90°. So the slope is large.

The angle is large. In mathematics, the least positive angle of the ridge formed by the intersection of two straight lines (or vectors) is called the angle between these two straight lines (or vectors), which is usually denoted as .

The greater the slope, the greater the degree of inclination.

1. Judge the size of the slope.

It is to judge the size of k, that is, to look at the angle between the straight line and the x-axis.

1. The larger the angle, the greater the slope, and conversely, the smaller the angle, the smaller the slope.

2. The slope is also the meaning of the angle of tan, and the image of tan is monotonically increasing from 0 to 90°. So the slope is large, the angle is large.

2. Determine the positive and negative slopes.

2. Positive and negative judgment of curve slope: the tangent of the point on the curve.

The slope of the line in which it is located.

, the slope is positive; k 0, the slope is negative.

When the inclination angle is 0-90 degrees, the slope of the shirt increases with the increase of the inclination angle. If the tilt angle is 0, the slope is 0. When the inclination angle is 90 degrees, the slope is infinite.

When the tilt angle is 90-180 degrees, the slope also increases with the tilt angle, but the slope increases from negative infinity to 0.

Introduction to Slope: The amount of the amount that represents the degree to which 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 (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.

Also known as the "angular coefficient", it is the tangent of the positive angle of a straight line to the abscissa axis, reflecting the inclination of the straight line to the horizontal plane.

Introduction to Tilt Angle:

In the plane Cartesian coordinate system, when the line L intersects the X axis, we take the X axis as the reference, and the angle a between the positive direction of the X axis and the upward direction of the line L is called the angle of inclination of the line L.

The value range of the tilt angle:

The angle of inclination is not a straight line of 90°, and the tangent of its angle of inclination is called the slope of the line. The slope of a straight line is often expressed or durable k

Methods of comparison:

1. When the straight line extends from the bottom left to the top right, the steeper the slope, the greater the slope, and the smaller the slope, the smaller the slope.

2. When the straight line extends from the upper left to the lower right, the larger the slope, the smaller the slope, and the smaller the slope, the greater the slope.

In the first case, the slope is always positive, and in the second case, the slope is always negative, and the slope is 0 when the line is parallel to the abscissa axis, and the slope does not exist when the vertical gear of the line is older than the abscissa axis.

The slope represents the amount of inclination of a straight line with respect to the coordinate axis, and it is usually expressed as the tangent of the angle between the line and the coordinate axis, or the ratio of the difference between the ordinate and the abscissa of two points.

The slope is used to measure the slope of a slope. Mathematically, the slope of a straight line is equal everywhere, and it is a measure of how inclined a straight line is. Through algebra and geometry, the slope of a straight line can be calculated; The slope of the previous point of the curve reflects how quickly the variables of the curve change at that point.

Using calculus, you can calculate the slope of any point in a curve. The concept of the slope of a straight line is equivalent to the slope in civil engineering and geography. The inclination angle is not a straight line of 90 degrees to have a slope.

1: When the straight line extends from the bottom left to the top right, the steeper the wheel or slope, the greater the slope, and the smaller the slope, the smaller the slope.

2. When the straight line extends from the upper left to the lower right, the larger the slope, the smaller the slope, and the smaller the slope, the greater the slope.

The slope of the first hail is always positive, and the slope is always negative in the second case. It is important to note that the slope is 0 when the straight source bridge line is parallel to the x-axis, and the slope does not exist when the line is perpendicular to the x-axis.