CN202939853U

CN202939853U - Inverse function demonstrator of cotangent function

Info

Publication number: CN202939853U
Application number: CN 201220753088
Authority: CN
Inventors: 赵永建; 张向平; 韦渤; 傅菲菲
Original assignee: Jinhua Polytechnic
Current assignee: Jinhua Polytechnic
Priority date: 2012-12-06
Filing date: 2012-12-06
Publication date: 2013-05-15
Anticipated expiration: 2022-12-06

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

The inverse function demonstrator of cotangent function

Technical field

The utility model relates to the education and instruction apparatus, and particularly a kind of inverse function demonstrator of cotangent function, can make the student when the inverse function of learning function, understands very intuitively the contrafunctional geometric meaning of cotangent function.

Background technology

The student has three steps when asking the inverse function of function y=f (x): first solve x=f (y); Again x is rewritten into y, y is rewritten into x; At last with the codomain of function as contrafunctional field of definition, with the field of definition of function as contrafunctional codomain.When the student asks the inverse function of function in learning higher mathematics, if teaching aid demonstration intuitively can be arranged, have good effect, the inverse function demonstrator of described cotangent function can address this problem, can demonstrate out the inverse function figure of function visually, and understand function graph position relation contrafunctional with it and geometric meaning in same plane right-angle coordinate.

The utility model content

In order to enrich the education and instruction apparatus, solve in higher mathematics and ask more contrafunctional apparent problem, the utility model provides a kind of inverse function demonstrator of cotangent function, can demonstrate out the inverse function figure of function visually, and make the student understand function graph position relation contrafunctional with it and geometric meaning in same plane right-angle coordinate.

The scheme that the utility model adopts is:

The inverse function demonstrator of cotangent function mainly is made of base, slot frame, glass plate, described slot frame is connected in above described base, described slot frame has orthogonal kerve and side channel, described glass plate is rectangle, have plane right-angle coordinate and cotangent function y=cot x 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 to the distance on limit, described glass plate left side, and described glass plate has identical two.We know, when asking the inverse function of function y=cot x, first obtain x=arc cot y; Be rewritten as again y=arc cot x; At last with the codomain of function as contrafunctional field of definition, the field of definition of function as contrafunctional codomain, is obtained function y=cot x, x ∈ (0, inverse function y=arc cot x π), x ∈ (∞ ,+∞).Said process is demonstrated with the inverse function demonstrator of described cotangent function: after first a described glass plate being extracted out from described slot frame, the plane is rotated counterclockwise 90 degree, then turns back to after the horizontal rotary turnback; Perhaps the plane dextrorotation turn 90 degrees, then turns back to after vertical rotary 180 degree, has at this moment demonstrated the figure of the inverse function y=arc cotx of function y=cot x in same plane right-angle coordinate.

The beneficial effects of the utility model are:

The inverse function demonstrator of cotangent function is reasonable in design, and the simple structure cost is low, can demonstrate out the inverse function figure of function visually, can make the student understand function graph position relation contrafunctional with it and geometric meaning in same plane right-angle coordinate.

Description of drawings

Further illustrate below in conjunction with figure of the present utility model:

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

Fig. 2 is the schematic diagram of described glass plate;

Fig. 3 is that the described glass plate plane of Fig. 2 is rotated counterclockwise 90 schematic diagram when spending;

Fig. 4 is the schematic diagram after the described glass plate horizontal rotary turnback of Fig. 3;

Fig. 5 is the schematic diagram after the described glass plate of Fig. 4 turns back to described slot frame again.

In figure, 1. base, 2. slot frame, 3. glass plate, 4. glass plate left side limit, 5. glass plate base.

Embodiment

The inverse function demonstrator schematic diagram of cotangent function as described in as Fig. 1 being, mainly consisted of by base (1), slot frame (2), glass plate (3), described slot frame (2) is connected in above described base (1), and described slot frame (2) has orthogonal kerve and side channel.

The schematic diagram of glass plate as described in as Fig. 2 being, described glass plate (3) is rectangle, have plane right-angle coordinate and cotangent function y=cot x on described glass plate interval (0, figure in 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).

As Fig. 3 be Fig. 2 as described in the glass plate plane be rotated counterclockwise 90 schematic diagram when spending, described glass plate (3) has identical two, Fig. 3 is after a described glass plate is extracted out from described slot frame, the plane is rotated counterclockwise 90 schematic diagram when spending.

As Fig. 4 be Fig. 3 as described in schematic diagram after glass plate horizontal rotary turnback, be namely the rear view of Fig. 3.

As Fig. 5 be Fig. 4 as described in glass plate turn back to again as described in schematic diagram after the slot frame, as seen demonstrated the figure of the inverse function y=arc cot x of function y=cot x in same plane right-angle coordinate, the figure of the figure of function y=cot x and inverse function y=arc cot x is symmetrical about y=x.

Teacher's figure contrafunctional with it according to function graft when demonstration carries out about the y=x symmetry, step: first extract a described glass plate out plane from described slot frame and be rotated counterclockwise 90 degree, then turn back to after the horizontal rotary turnback; Perhaps the plane dextrorotation turn 90 degrees, then turns back to after vertical rotary 180 degree.Because 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), after having guaranteed a described glass plate is turned back to, plane right-angle coordinate initial point and the coordinate axis of two described glass plates are all overlapped, drill visually being illustrated in function and its inverse function figure in same plane right-angle coordinate, can make the student understand function graph position relation contrafunctional with it and geometric meaning in same plane right-angle coordinate.

Claims

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.