CN202939853U - Inverse function demonstrator of cotangent function - Google Patents

Inverse function demonstrator of cotangent function Download PDF

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Publication number
CN202939853U
CN202939853U CN 201220753088 CN201220753088U CN202939853U CN 202939853 U CN202939853 U CN 202939853U CN 201220753088 CN201220753088 CN 201220753088 CN 201220753088 U CN201220753088 U CN 201220753088U CN 202939853 U CN202939853 U CN 202939853U
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CN
China
Prior art keywords
function
glass plate
cotangent
demonstrator
glass plates
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Expired - Fee Related
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CN 201220753088
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Chinese (zh)
Inventor
赵永建
张向平
韦渤
傅菲菲
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Jinhua Polytechnic
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Jinhua Polytechnic
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Priority to CN 201220753088 priority Critical patent/CN202939853U/en
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Publication of CN202939853U publication Critical patent/CN202939853U/en
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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 (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.
CN 201220753088 2012-12-06 2012-12-06 Inverse function demonstrator of cotangent function Expired - Fee Related CN202939853U (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN 201220753088 CN202939853U (en) 2012-12-06 2012-12-06 Inverse function demonstrator of cotangent function

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN 201220753088 CN202939853U (en) 2012-12-06 2012-12-06 Inverse function demonstrator of cotangent function

Publications (1)

Publication Number Publication Date
CN202939853U true CN202939853U (en) 2013-05-15

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Family Applications (1)

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CN 201220753088 Expired - Fee Related CN202939853U (en) 2012-12-06 2012-12-06 Inverse function demonstrator of cotangent function

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104332085A (en) * 2014-11-25 2015-02-04 南京工业职业技术学院 Anti-tangent, cotangent, secant and cosecant function demonstrating and graph drawing instrument
RU2755082C1 (en) * 2021-02-12 2021-09-13 Олег Александрович Поваляев Measuring unit for voltage measurement
RU2755547C1 (en) * 2021-02-12 2021-09-17 Олег Александрович Поваляев Measuring module for measuring humidity

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104332085A (en) * 2014-11-25 2015-02-04 南京工业职业技术学院 Anti-tangent, cotangent, secant and cosecant function demonstrating and graph drawing instrument
RU2755082C1 (en) * 2021-02-12 2021-09-13 Олег Александрович Поваляев Measuring unit for voltage measurement
RU2755547C1 (en) * 2021-02-12 2021-09-17 Олег Александрович Поваляев Measuring module for measuring humidity

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C17 Cessation of patent right
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20130515

Termination date: 20131206