CN202939853U  Inverse function demonstrator of cotangent function  Google Patents
Inverse function demonstrator of cotangent function Download PDFInfo
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 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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 function
 glass plate
 cotangent
 demonstrator
 glass plates
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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
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 rightangle 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 rightangle 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 rightangle coordinate and cotangent function y=cot x on described glass plate interval (0, figure π), the initial point of described plane rightangle 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 rightangle 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 rightangle 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 rightangle coordinate and cotangent function y=cot x on described glass plate interval (0, figure in π), the initial point of described plane rightangle 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 rightangle 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 rightangle 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 rightangle 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 rightangle coordinate, can make the student understand function graph position relation contrafunctional with it and geometric meaning in same plane rightangle 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 rightangle coordinate and cotangent function y=cotx on described glass plate interval (0, figure π), the initial point of described plane rightangle 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.
Priority Applications (1)
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CN 201220753088 CN202939853U (en)  20121206  20121206  Inverse function demonstrator of cotangent function 
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CN 201220753088 CN202939853U (en)  20121206  20121206  Inverse function demonstrator of cotangent function 
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CN202939853U true CN202939853U (en)  20130515 
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CN 201220753088 Expired  Fee Related CN202939853U (en)  20121206  20121206  Inverse function demonstrator of cotangent function 
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Cited By (3)
Publication number  Priority date  Publication date  Assignee  Title 

CN104332085A (en) *  20141125  20150204  南京工业职业技术学院  Antitangent, cotangent, secant and cosecant function demonstrating and graph drawing instrument 
RU2755082C1 (en) *  20210212  20210913  Олег Александрович Поваляев  Measuring unit for voltage measurement 
RU2755547C1 (en) *  20210212  20210917  Олег Александрович Поваляев  Measuring module for measuring humidity 

2012
 20121206 CN CN 201220753088 patent/CN202939853U/en not_active Expired  Fee Related
Cited By (3)
Publication number  Priority date  Publication date  Assignee  Title 

CN104332085A (en) *  20141125  20150204  南京工业职业技术学院  Antitangent, cotangent, secant and cosecant function demonstrating and graph drawing instrument 
RU2755082C1 (en) *  20210212  20210913  Олег Александрович Поваляев  Measuring unit for voltage measurement 
RU2755547C1 (en) *  20210212  20210917  Олег Александрович Поваляев  Measuring module for measuring humidity 
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C14  Grant of patent or utility model  
GR01  Patent grant  
C17  Cessation of patent right  
CF01  Termination of patent right due to nonpayment of annual fee 
Granted publication date: 20130515 Termination date: 20131206 