CN202939853U - Inverse function demonstrator of cotangent function - Google Patents

Abstract

The utility model relates to a teaching appliance. An inverse function demonstrator of a cotangent function mainly comprises a base, a slot frame, and glass plates. The slot frame is connected to an upper face of the base. The slot frame has a bottom slot and a side slot which are perpendicular to each other. The glass plates are rectangular. A plane rectangular coordinate system and a graph of the cotangent function (y equals to cot x) in the interval [0, pi] are provided on the glass plates. The distance from the origin of the plane rectangular coordinate system to a left side edge of the glass plates is equal to the distance from the origin of the plane rectangular coordinate system to a bottom edge of the glass plates. The number of the glass plates is two. The inverse function demonstrator of the cotangent function is reasonably designed, is simple in structure and low in cost, can vividly demonstrate the inverse function graph of the function, and can make students understand the graph position relation and the geometric significance of the function and the inverse function thereof in the same plane rectangular coordinate system.

Description

Demonstration instrument for inverse function of cotangent function

technical field

The utility model relates to an educational teaching appliance, in particular to an inverse function demonstrator of a cotangent function, which enables students to intuitively understand the geometric meaning of the inverse function of a cotangent function when learning the inverse function of a function.

Background technique

When students seek the inverse function of the function y=f(x), there are three steps: first solve x=f(y); then rewrite x into y, and rewrite y into x; finally, use the value range of the function as the inverse function Domain, the domain of the function is used as the domain of the inverse function. When students learn the inverse function of a function in advanced mathematics, if they can have an intuitive teaching aid demonstration, there will be a good effect. The inverse function demonstrator of the cotangent function can solve this problem and can demonstrate the function visually. The graph of the inverse function of the function, and understand the graph position relationship and geometric meaning of the function and its inverse function in the same plane Cartesian coordinate system.

Utility model content

In order to enrich educational and teaching tools and solve some intuitive problems of inverse function in advanced mathematics, the utility model provides an inverse function demonstrator of cotangent function, which can vividly demonstrate the inverse function graph of the function, and make students understand the inverse function in the same time. The graphic position relationship and geometric meaning of a function and its inverse function in a plane Cartesian coordinate system.

The scheme that the utility model adopts is:

The inverse function demonstrator of the cotangent function is mainly composed of a base, a slot frame, and a glass plate. The slot frame is connected to the base. The slot frame has bottom grooves and side grooves perpendicular to each other. The glass The plate is a rectangle, and the glass plate has a plane Cartesian coordinate system and a figure of a cotangent function y=cot x in the interval (0, π), the distance from the origin of the plane Cartesian coordinate system to the left side of the glass plate The distance is equal to the distance to the bottom edge of the glass panes, which have the same two pieces. We know that when finding the inverse function of the function y=cot x, first find out x=arc cot y; then rewrite it as y=arc cot x; As the value range of the inverse function, the inverse function y=arc cot x, x ∈ (-∞, +∞) of the function y=cot x, x∈(0, π) is obtained. The above process is demonstrated by using the inverse function demonstrator of the cotangent function: firstly, after pulling out a piece of the glass plate from the slot frame, rotate the plane counterclockwise 90 degrees, and then insert it back after horizontally rotating 180 degrees; or Rotate the plane clockwise by 90 degrees, and then insert it back after rotating it vertically by 180 degrees. At this time, the graph of the inverse function y=arc cotx of the function y=cot x is displayed in the same plane Cartesian coordinate system.

The beneficial effects of the utility model are:

The inverse function demonstrator of the cotangent function has reasonable design, simple structure and low cost, and can vividly demonstrate the inverse function graph of the function, enabling students to understand the graph position relationship and geometric meaning of the function and its inverse function in the same plane Cartesian coordinate system .

Description of drawings

Below in conjunction with the figure of the present utility model further explanation:

Fig. 1 is the inverse function demonstrator schematic diagram of described cotangent function;

Figure 2 is a schematic diagram of the glass plate;

Fig. 3 is a schematic diagram when the plane of the glass plate in Fig. 2 is rotated 90 degrees counterclockwise;

Fig. 4 is a schematic diagram of the glass plate shown in Fig. 3 rotated horizontally by 180 degrees;

Fig. 5 is a schematic diagram of the glass plate in Fig. 4 after being inserted back into the slot frame.

In the figure, 1. the base, 2. the slot frame, 3. the glass plate, 4. the left side of the glass plate, and 5. the bottom edge of the glass plate.

Detailed ways

Figure 1 is a schematic diagram of the inverse function demonstrator of the cotangent function, mainly composed of a base (1), a slot frame (2), and a glass plate (3), and the slot frame (2) is connected to the base (1) Above, the slot frame (2) has bottom grooves and side grooves perpendicular to each other.

Fig. 2 is the schematic diagram of described glass plate, and described glass plate (3) is rectangle, and described glass plate has plane Cartesian coordinate system and cotangent function y=cot x in the figure in interval (0, π), The distance from the origin of the plane rectangular coordinate system to the left edge (4) of the glass plate is equal to the distance to the bottom edge (5) of the glass plate.

Figure 3 is a schematic diagram of the plane of the glass plate in Figure 2 when it is rotated 90 degrees counterclockwise, the glass plate (3) has two identical pieces, and Figure 3 is a drawing out of one of the glass plates from the slot frame Finally, the schematic diagram when the plane is rotated 90 degrees counterclockwise.

FIG. 4 is a schematic diagram of the glass plate in FIG. 3 horizontally rotated by 180 degrees, which is the rear view of FIG. 3 .

Fig. 5 is the schematic diagram after the described glass plate of Fig. 4 is inserted back into described slot frame again, it can be seen that the graph of the inverse function y=arc cot x of function y=cot x has been shown in the same plane Cartesian coordinate system , the graph of the function y=cot x and the graph of the inverse function y=arc cot x are symmetrical about y=x.

When the teacher demonstrates, it is based on the graph of the function and its inverse function being symmetrical about y=x. The steps are: firstly rotate a piece of the glass plate out of the slot frame counterclockwise by 90 degrees, and then rotate it horizontally by 180 degrees Insert it back; or rotate the plane 90 degrees clockwise, then rotate it vertically 180 degrees and insert it back. Since the distance from the origin of the plane Cartesian coordinate system to the left edge (4) of the glass plate is equal to the distance to the bottom edge (5) of the glass plate, it is ensured that a piece of the glass plate can be used after being inserted back. The plane Cartesian coordinate system origin and the coordinate axes of the two described glass plates are all coincident, which vividly demonstrates the function and its inverse function graph in the same plane Cartesian coordinate system, and enables students to understand the function and its inverse function in the same plane Cartesian coordinate system. The graph position relationship and geometric meaning of the inverse function.

Claims (2)

1. the inverse function demonstrator of a cotangent function, mainly by base, the slot frame, glass plate consists of, it is characterized in that: described slot frame (2) is connected in above described base (1), described slot frame (2) has orthogonal kerve and side channel, described glass plate (3) is rectangle, have plane right-angle coordinate and cotangent function y=cotx on described glass plate interval (0, figure π), the initial point of described plane right-angle coordinate equates with distance to described glass plate base (5) to the distance on described glass plate limit, left side (4).

2. the inverse function demonstrator of cotangent function according to claim 1, it is characterized in that: described glass plate (3) has identical two.

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