CN106898200A - A kind of trigonometric function image converts demenstration method and device - Google Patents
A kind of trigonometric function image converts demenstration method and device Download PDFInfo
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- CN106898200A CN106898200A CN201710291185.XA CN201710291185A CN106898200A CN 106898200 A CN106898200 A CN 106898200A CN 201710291185 A CN201710291185 A CN 201710291185A CN 106898200 A CN106898200 A CN 106898200A
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- 239000004744 fabric Substances 0.000 claims abstract description 58
- 239000011324 bead Substances 0.000 claims abstract description 12
- 238000006243 chemical reaction Methods 0.000 description 15
- 230000003068 static effect Effects 0.000 description 6
- 238000010586 diagram Methods 0.000 description 5
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Classifications
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/02—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics
- G09B23/04—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics for geometry, trigonometry, projection or perspective
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Abstract
A kind of trigonometric function image converts apparatus for demonstrating,It is characterized in that,Including housing,Outer inframe is provided with telescopically adjustable demonstration cloth,Demonstration cloth upper and lower side is distributed with many first silk threads with elasticity,Housing top and bottom are respectively equipped with an axis of guide,Axis of guide two ends are placed in housing outside,Housing top and bottom are respectively equipped with the first guide rail,Multiple beads that can be slided in the first guide rail are provided with first guide rail,Bead is provided with the first sliding block,The first aperture that first sliding block is communicated before and after being provided with,Housing back is installed with support frame,Support frame top and bottom are provided with multiple second orifices,Support frame is provided with fixing axle,Fixing axle is provided with line wheel,First silk thread sequentially passes through the first aperture,Second orifice,First silk thread is connected with line wheel,The axis of guide is provided with the second guide rail for being placed in housing or so two ends,Second guide rail is the structure that can be slided along the axis of guide,Multiple second sliding blocks are provided with second guide rail,Many second silk threads are connected between second sliding block and demonstration cloth.
Description
Technical field
The present invention relates to the instructional technology field of Mathematical Modeling, particularly a kind of trigonometric function image conversion demenstration method and
Device.
Background technology
For Mathematical Modeling, it is directed to the feature or quantity dependence with reference to certain things system, summarizes or approximate
Give expression to a kind of mathematic(al) structure, the present invention inquires into emphatically the transformation relation between trigonometric function image.
At present, it is according on textbook by teacher for the explanation major part of the conversion process of trigonometric function in educational work
Two methods of picture understand conversion process in static curve and blackboard, and conditional teacher shown using multimedia projector
Conversion process, the teacher for also having only a few makes Dynamic Graph to show conversion process with the plenty of time using computer.
But, above method all has the following disadvantages：
1st, static map easily shows, but is not easy to demonstrate conversion process, and student does not allow readily understood.
2nd, multimedia represents with conversion process, but can need multimedia equipment, it has not been convenient to carry, expensive, to religion
Learn on-the-spot teaching equipment requirement too high.
Although the 3, Dynamic Graph can demonstrate dynamic process, needs take a significant amount of time and energy, and the result for converting
It is limited.
So, the invention provides a kind of trigonometric function image conversion demenstration method and device.
The content of the invention
For above-mentioned situation, to overcome the defect of prior art, the present invention to provide a kind of trigonometric function image conversion demonstration
Method and apparatus, effectively solve the not intelligible problem of static map during the conversion explanation of trigonometric function image, not restricted
On-the-spot teaching equipment and it is easy to carry about with one in teaching, it is not required that the plenty of time is wasted in making Dynamic Graph, while can be adjustable
In the range of arbitrarily convert.
The present invention includes housing, and outer inframe is provided with telescopically adjustable demonstration cloth, and demonstration cloth upper and lower side is distributed with many bands
First silk thread of elasticity, housing top and bottom are respectively equipped with an axis of guide, and axis of guide two ends are placed in housing outside, housing
Top and bottom are respectively equipped with the first guide rail, and multiple beads that can be slided in the first guide rail, bead are provided with the first guide rail
The first sliding block is provided with, the first aperture that the first sliding block is communicated before and after being provided with, housing back is installed with support frame, supports
Frame top and bottom are provided with multiple second orifices, and support frame is provided with fixing axle, and fixing axle is provided with line wheel, and the first silk thread is successively
Through the first aperture, second orifice, the first silk thread is connected with line wheel, and the axis of guide is provided with and is placed in the second of housing or so two ends and leads
Rail, the second guide rail is the structure that can be slided along the axis of guide, and multiple second sliding blocks, the second sliding block and demonstration cloth are provided with the second guide rail
Between be connected with many second silk threads.
Preferably, described outer inframe is provided with and is placed in the demonstration dismountable flat board in cloth rear, and one is shown on flat board admittedly
Fixed constant SIN function y=Sin x curves, outer inframe is provided with two graduated scales being placed between demonstration cloth and flat board, graduated scale
It is the structure that can be slided along housing.
Preferably, a sine curve of y=Sin x is shown on described demonstration cloth.
It is a kind of to realize the method that trigonometric function image converts apparatus for demonstrating, it is characterised in that to comprise the following steps：First
Step, adjustment demonstration cloth, makes the curve on demonstration cloth be overlapped with the sine curve y=Sin x on flat board；Second step, zeroing, will adjust
The starting point of whole good curve is overlapped with the zero point on graduated scale, and graduated scale is fixed；3rd step, rotates line wheel, and line wheel is by first
Silk thread is coiled, and in the presence of the first silk thread, with the change of demonstration cloth longitudinal size, sine curve is by y=on demonstration cloth
Sin x become y=A Sin x；4th step, moves left and right the second guide rail, the second sliding block in the second guide rail by the second silk thread come
Cross directional stretch demonstrates cloth, and the sine curve on demonstration cloth becomes y=A Sin ω x by y=A Sin x；5th step, pulls the axis of guide,
The axis of guide is set to drive the second guide rail to move left and right, the distance between two second guide rails do not change, in curve y=A Sin ω
X realizes moving left and right in the case of not deforming upon, and sine curve y=A Sin ω x become y=A Sin（ωx+φ）.
Clever structure of the present invention, it is novel, easily make, it is easy to carry, effectively solve the change of trigonometric function image
The not intelligible problem of static map during explanation is changed, without being bound by teaching on-the-spot teaching equipment, it is not required that plenty of time wave
Take and making Dynamic Graph, while can arbitrarily be converted in adjustable extent.
Brief description of the drawings
Fig. 1 is front view schematic diagram of the present invention.
Fig. 2 is rearview partial schematic diagram of the present invention.
Fig. 3 is partial schematic diagram of the present invention.
Fig. 4 is the sectional view schematic diagram of the first guide rail of the invention 5.
Fig. 5 is the sectional view schematic diagram of the first guide rail of the invention 12.
Specific embodiment
For the present invention foregoing and other technology contents, feature and effect, in following cooperation with reference to figures 1 through Fig. 5 pairs
In the detailed description of embodiment, can clearly present.The structure content being previously mentioned in following examples, is attached with specification
Figure is reference.
Each exemplary embodiment of the invention is described below with reference to accompanying drawings.
Embodiment one, the present invention converts apparatus for demonstrating, including housing 1 for a kind of trigonometric function image, is placed with housing 1
Telescopically adjustable demonstration cloth 2, the demonstration upper and lower side of cloth 2 is distributed with many first silk threads 3, the first silk thread 3 be it is elastic, outward
The top and bottom of frame 1 are separately installed with an axis of guide 4, and the axis of guide 4 can do horizontal axis motion, and the axis of guide 4 is than housing 1
Length will be grown, and the two ends of the axis of guide 4 are placed in the outside of housing 1, and the top and bottom of housing 1 are respectively equipped with the first guide rail 5,
Multiple beads 6 are placed with first guide rail 5, bead 6 can be slided in the first guide rail 5, and the first sliding block 7 is provided with bead 6,
First sliding block 7 constitutes the structure that can be slided in the first guide rail 5 with bead 6, and the first aperture 8 is provided with the first sliding block 7, the
One aperture 8 be it is front and rear communicate, the back of housing 1 is installed with support frame 9, and the top and bottom of support frame 9 are provided with multiple the
Two apertures 801, are fixed with fixing axle 10 on support frame 9, line wheel 11 is provided with fixing axle 10, and line wheel 11 can be around fixing axle 10
Rotate, the first silk thread 3 sequentially passes through the first aperture 8, second orifice 801, and the first silk thread 3 is connected with line wheel 11, and line wheel 11 is rotated
Meeting by the first silk thread 3 coil get up, while the first silk thread 3 can pull demonstration cloth 2 do longitudinal stretching, be provided with the axis of guide 4
Second guide rail 12, the second guide rail 12 is individually positioned in the left and right two ends of housing 1, and the second guide rail 12 can be slided along the axis of guide 4, and second
Multiple second sliding blocks 13 are placed with guide rail 12, the second sliding block 13 can be slided along the second guide rail 13, the second sliding block 13 with drill
Show and be connected with many second silk threads 14 between cloth 2.
Embodiment two, on the basis of embodiment one, flat board 15 is provided with described housing 1, and flat board 15 is placed on drills
Show the rear of cloth 2, flat board 15 encloses one block of dismountable plate, and a changeless SIN function y=Sin x is shown on flat board 15
Two graduated scales 16 are installed, two graduated scales 16 are mutually perpendicular to place, and graduated scale 16 is placed on demonstration cloth 2 in curve, housing 1
Between flat board 15, graduated scale 16 can be slided along housing 1.
Embodiment three, on the basis of embodiment two, the sine that a y=Sin x is shown on described demonstration cloth 2 is bent
Line.
Example IV, the present invention realizes the method that trigonometric function image converts apparatus for demonstrating for a kind of, it is characterised in that bag
Include following steps：The first step, adjustment demonstration cloth 2 makes the sine curve y=Sin x weights on the curve and flat board 15 on demonstration cloth 2
Close；Second step, zeroing, the starting point of the curve that will be adjusted overlaps with the zero point on graduated scale 16, graduated scale 16 is fixed；3rd
Step, rotates line wheel 11, and the first silk thread 3 is coiled by line wheel 11, in the presence of the first silk thread 3, with the demonstration longitudinal ruler of cloth 2
Very little change, sine curve becomes y=A Sin x by y=Sin x on demonstration cloth 2；4th step, moves left and right the second guide rail 12, the
The second sliding block 13 in two guide rails 12 demonstrates cloth 2 by the second silk thread 14 come cross directional stretch, and the sine curve on demonstration cloth 2 is by y=
A Sin x become y=A Sin ω x；5th step, pulls the axis of guide 4, makes the axis of guide 4 drive the second guide rail 12 to move left and right, two
The distance between second guide rail 12 does not change, and realizes that left and right is moved in the case where curve y=A Sin ω x are not deformed upon
Dynamic, sine curve y=A Sin ω x become y=A Sin（ωx+φ）.
It is well known that in daily research work, people often can be summarized numerous and diverse data, to set up affairs between it is pure
Pure relation, that is, function model, trigonometric function are one of six class basic elementary functions in function, therefore, in education and instruction
Link, trigonometric function is regarded as the difficult point and emphasis of examination, and teacher can emphatically explain the conversion process of trigonometric function and trigonometric function,
For student, understand trigonometric function just by must GPRS trigonometric function essential y=Sin x and be transformed into by y=Sin x
y=A Sin（ωx+φ）Process.The stretching peace that the present invention passes through the demonstration cloth 2 to showing known trigonometric function curve
Move, realize trigonometric function y=Sin x and y=A Sin（ωx+φ）Between conversion process, help student understand trigonometric function
Essence.
Housing 1 is a frame for rectangle, and the inner side of housing 1 is provided with the groove slided for two graduated scales 16, two graduated scales 16
Can be slided along the level of housing 1 respectively and slip vertically, staggered before and after two graduated scales 16, two graduated scales 16 are mutual when sliding
Do not interfere.
Described demonstration cloth 2 is a telescopic transparent material, and a curve of y=Sin x is shown on demonstration cloth 2,
Curve also has the flexible of respective direction with the flexible of demonstration cloth 2.The demonstration upper and lower side of cloth 2 is evenly arranged the first a plurality of silk thread
3, the first silk thread 3 can affect demonstration cloth 2 to realize demonstrating the flexible of cloth 2 with this.
The top and bottom of housing 1 are both provided with the axis of guide 4, and the axis of guide 4 is arranged on the lower section of the first guide rail 5, and the axis of guide 4 can be with
Horizontal axis motion is done, the axis of guide 4 runs through the second guide rail 5, and the second guide rail 5 can be slided along the axis of guide 4, on the second guide rail 5
There is Positioning screw lower end, and when Positioning screw compresses the axis of guide 4, now, the axis of guide 4 is maintained static with the second guide rail 5, demonstrates cloth 2
The length of horizontal direction is also just secured, and when housing screw is unclamped, the second guide rail 5 can be along the axis of guide 4 slidably.
The upper and lower ends of housing 1 are provided with the sliding block 7 of bead 6 and first, and the first sliding block 7 can be as bead 6 be in the first guide rail 5
Interior slip, the first silk thread 3 sequentially passes through demonstration cloth 2, the first aperture 8, second orifice 801 and line wheel 11, and line wheel 11 is rotated, by the
One silk thread 3 is coiled up, and the first silk thread 3 affects demonstration cloth 2 to do longitudinal stretching.
Multiple second sliding blocks 13, the second sliding block 13 and demonstration cloth 2 are placed with second guide rail 12 of the left and right sides of housing 1
Between connected by the second silk thread 14, the horizontal movement of the second guide rail 12 can drive the motion of multiple second sliding blocks 13, and second slides
Block 13 affects the second silk thread 14, cloth 2 is demonstrated in the case where many second silk threads 14 are acted on and is also occurred flexible or is translated.
When two the second guide rails 5 are fixed in the presence of housing screw with the axis of guide 4, two axis of guides are now moved left and right
4, now size dimension will not change demonstration cloth, but can realize translation, and so far, the left and right of function curve image translates
To realize.
Flat board 15 is one piece of flat board of demonstration fixed curve, and top shows a curve that will not be deformed upon, flat board
15 effect is, when demonstration cloth 2 is transformed into final result, by the curve comparison on flat board 15 and can to demonstrate the song on cloth 2
Line is analyzed, and allows student with being readily appreciated that.
One containment vessel can be installed on support frame 9, multiple suckers can be installed on containment vessel.When Yanshi, sucker
Can adsorb on the wall or desk, convenient operation.
It is worth noting that, while demonstration cloth 2 realizes longitudinal stretching, the second sliding block 13 in the second guide rail 5
Also corresponding motion is had, is placed because unbalance stress causes demonstration cloth 2 uncontrollable unexpected deformation occur, influence teaching efficiency,
Similarly, when demonstration cloth 2 realizes horizontal extension, the first silk thread 3 can pull the first sliding block 7 to be slided along the first guide rail 5.By upper
Method is stated, the conversion process between trigonometric function curve is really shown as far as possible.
A kind of trigonometric function image conversion demenstration method and device that the present invention is provided, effectively solve trigonometric function graph
As conversion explanation during the not intelligible problem of static map, can arbitrarily convert in adjustable extent and without being bound by impart knowledge to students now
Field teaching equipment, and be easy to carry about with one, it is not required that the plenty of time is wasted in the specific Dynamic Graph of making.
Although it will be noted that on the basis of with reference to each embodiment, the present invention has been described simultaneously in the description
And be illustrated in the accompanying drawings, but it will be understood to those skilled in the art that above-described embodiment is only preferred embodiment,
Some of embodiment technical characteristic to solve specific technical problem may it is not necessary to, such that it is able to without or save
Slightly these technical characteristics are without the solution of influence technique problem or the formation of technical scheme.Further, one embodiment
Feature, key element and/or function can be with the feature of other one or more embodiments, key element and/or appropriate mutual groups of function
Close, with reference to or coordinate, unless the combination, with reference to or cooperation can not substantially implement.
Claims (4)
1. a kind of trigonometric function image converts apparatus for demonstrating, it is characterised in that including housing（1）, housing（1）Inside it is provided with scalable
The demonstration cloth of regulation（2）, demonstrate cloth（2）Upper and lower side is distributed with many first silk threads with elasticity（3）, housing（1）Upper end is with
End is respectively equipped with an axis of guide（4）, the axis of guide（4）Two ends are placed in housing（1）Outside, housing（1）Distinguish top and bottom
It is provided with the first guide rail（5）, the first guide rail（5）Inside being provided with multiple can be in the first guide rail（5）The bead of interior slip（6）, bead（6）
It is provided with the first sliding block（7）, the first sliding block（7）The first aperture communicated before and after being provided with（8）, housing（1）Back fixedly mounts
There is support frame（9）, support frame（9）Top and bottom are provided with multiple second orifices（801）, support frame（9）It is provided with fixing axle
（10）, fixing axle（10）It is provided with line wheel（11）, the first silk thread（3）Sequentially pass through the first aperture（8）, second orifice（801）, the
One silk thread（3）With line wheel（11）Connection, the axis of guide（4）It is provided with and is placed in housing（1）Second guide rail at left and right two ends（12）, second
Guide rail（12）For can be along the axis of guide（4）The structure of slip, the second guide rail（12）Inside it is provided with multiple second sliding blocks（13）, the second sliding block
（13）With demonstration cloth（2）Between be connected with many second silk threads（14）.
2. a kind of trigonometric function image according to claim 1 converts apparatus for demonstrating, it is characterised in that described housing
（1）Inside it is provided with and is placed in demonstration cloth（2）The dismountable flat board in rear（15）, flat board（15）On show a changeless sine
Function y=Sin x curves, housing（1）Inside it is provided with and is placed in demonstration cloth（2）With flat board（15）Between two graduated scales（16）, scale
Chi（16）For can be along housing（1）The structure of slip.
3. a kind of trigonometric function image according to claim 2 converts apparatus for demonstrating, it is characterised in that described demonstration cloth
（2）On show a sine curve of y=Sin x.
4. it is a kind of to realize the method that trigonometric function image converts apparatus for demonstrating, it is characterised in that to comprise the following steps：The first step,
Adjustment demonstration cloth（2）, make demonstration cloth（2）On curve and flat board（15）On sine curve y=Sin x overlap；
Second step, zeroing, the starting point and graduated scale of the curve that will be adjusted（16）On zero point overlap, by graduated scale（16）Gu
It is fixed；
3rd step, rotates line wheel（11）, line wheel（11）By the first silk thread（3）Coiling is got up, in the first silk thread（3）In the presence of,
With demonstration cloth（2）The change of longitudinal size, demonstrates cloth（2）Upper sine curve becomes y=A Sin x by y=Sin x；
4th step, moves left and right the second guide rail（12）, the second guide rail（12）The second interior sliding block（13）By the second silk thread（14）
Carry out cross directional stretch demonstration cloth（2）, demonstrate cloth（2）On sine curve y=A Sin ω x are become by y=A Sin x；
5th step, pulls the axis of guide（4）, make the axis of guide（4）Drive the second guide rail（12）Move left and right, two the second guide rails（12）
The distance between do not change, realize moving left and right in the case where curve y=A Sin ω x are not deformed upon, sine curve y
=A Sin ω x become y=A Sin（ωx+φ）.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710291185.XA CN106898200B (en) | 2017-04-28 | 2017-04-28 | A kind of trigonometric function image conversion demenstration method and device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710291185.XA CN106898200B (en) | 2017-04-28 | 2017-04-28 | A kind of trigonometric function image conversion demenstration method and device |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106898200A true CN106898200A (en) | 2017-06-27 |
| CN106898200B CN106898200B (en) | 2017-12-08 |
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ID=59196608
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710291185.XA Expired - Fee Related CN106898200B (en) | 2017-04-28 | 2017-04-28 | A kind of trigonometric function image conversion demenstration method and device |
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| Country | Link |
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| CN (1) | CN106898200B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111161584A (en) * | 2020-02-26 | 2020-05-15 | 福建农林大学 | VR experiences aftershock simulation platform |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6132217A (en) * | 1998-12-23 | 2000-10-17 | Dickson; Marilyn M. | Method and apparatus for teaching relationship of trigonometric functions between unit circle and rectangular coordinate system |
| CN205318697U (en) * | 2015-12-28 | 2016-06-15 | 新余学院 | Demonstration teaching aid of functional limit for advanced math teaching |
| CN205943212U (en) * | 2016-04-12 | 2017-02-08 | 黑龙江工程学院 | Higher mathematics function demonstration teaching aid |
-
2017
- 2017-04-28 CN CN201710291185.XA patent/CN106898200B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6132217A (en) * | 1998-12-23 | 2000-10-17 | Dickson; Marilyn M. | Method and apparatus for teaching relationship of trigonometric functions between unit circle and rectangular coordinate system |
| CN205318697U (en) * | 2015-12-28 | 2016-06-15 | 新余学院 | Demonstration teaching aid of functional limit for advanced math teaching |
| CN205943212U (en) * | 2016-04-12 | 2017-02-08 | 黑龙江工程学院 | Higher mathematics function demonstration teaching aid |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111161584A (en) * | 2020-02-26 | 2020-05-15 | 福建农林大学 | VR experiences aftershock simulation platform |
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| Publication number | Publication date |
|---|---|
| CN106898200B (en) | 2017-12-08 |
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| CB03 | Change of inventor or designer information |
Inventor after: Wang Dongxiao Inventor after: Mao Beixing Inventor after: Wu Dayong Inventor after: Chang Juan Inventor before: Wang Xiaodong Inventor before: Mao Beixing Inventor before: Wu Dayong Inventor before: Chang Juan |
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Granted publication date: 20171208 Termination date: 20190428 |