CN106898200B - A kind of trigonometric function image conversion demenstration method and device - Google Patents
A kind of trigonometric function image conversion demenstration method and device Download PDFInfo
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- CN106898200B CN106898200B CN201710291185.XA CN201710291185A CN106898200B CN 106898200 B CN106898200 B CN 106898200B CN 201710291185 A CN201710291185 A CN 201710291185A CN 106898200 B CN106898200 B CN 106898200B
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- 238000006243 chemical reaction Methods 0.000 title claims description 21
- 239000004744 fabric Substances 0.000 claims abstract description 58
- 239000011324 bead Substances 0.000 claims abstract description 12
- 238000010586 diagram Methods 0.000 description 5
- 230000003068 static effect Effects 0.000 description 5
- 238000005516 engineering process Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- 241000252254 Catostomidae Species 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000005553 drilling Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
- 239000012780 transparent material Substances 0.000 description 1
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,More the first silk threads with elasticity are distributed with demonstration cloth upper and lower side,Housing top and bottom are respectively equipped with an axis of guide,Axis of guide both ends are placed on the outside of housing,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,First sliding block is provided with front and rear the first aperture communicated,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 left and right 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,More 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
It is to be directed to the feature or quantity dependence with reference to certain things system for mathematical modeling, 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, in educational work, the explanation for the conversion process of trigonometric function is largely according on textbook by teacher
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 make Dynamic Graph to show conversion process with the plenty of time using computer.
But above method all has the following disadvantages：
1st, static map is easily shown, but is not easy to demonstrate conversion process, and student does not allow readily understood.
2nd, show can be with conversion process for multimedia, but needs multimedia equipment, it has not been convenient to carry, it is expensive, and to religion
It is too high to learn on-the-spot teaching equipment requirement.
Although the 3, Dynamic Graph can demonstrate dynamic process, needs take a significant amount of time and energy, and the result converted
It is limited.
So the invention provides a kind of trigonometric function image conversion demenstration method and device.
The content of the invention
For the above situation, to overcome the defect of prior art, the present invention provides a kind of trigonometric function image conversion demonstration
Method and apparatus, static map is not readily understood during effectively solving the problems, such as the conversion explanation of trigonometric function image, not restricted
In teaching on-the-spot teaching equipment and it is easy to carry about with one, 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 more bands are distributed with demonstration cloth upper and lower side
First silk thread of elasticity, housing top and bottom are respectively equipped with an axis of guide, and axis of guide both ends are placed on the outside of housing, 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 sliding block is provided with front and rear the first aperture communicated, and 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 left and right ends and leads
Rail, the second guide rail are the structure that can be slided along the axis of guide, and the second guide rail is interior to be provided with multiple second sliding blocks, the second sliding block and demonstration cloth
Between be connected with more second silk threads.
Preferably, described outer inframe, which is provided with, 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 are provided with two graduated scales being placed between demonstration cloth and flat board, graduated scale
For the structure that can be slided along housing.
Preferably, y=Sin x sine curve is shown on described demonstration cloth.
A kind of method for realizing trigonometric function image conversion apparatus for demonstrating, it is characterised in that comprise the following steps：First
Step, adjustment demonstration cloth, makes the curve on demonstration cloth be overlapped with sine curve y=Sin x on flat board；Second step, zeroing, will be adjusted
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 coil get up, in the presence of the first silk thread, with demonstration cloth longitudinal size change, demonstrate cloth on sine curve by y=
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 demonstrated on cloth becomes y=A Sin ω x by y=A Sin x；5th step, the axis of guide is pulled,
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 and moved left and right that sine curve y=A Sin ω x become y=A Sin in the case of not deforming upon（ωx+φ）.
Clever structure of the present invention, it is novel, easily make, be easy to carry, effectively solve the change of trigonometric function image
The problem of static map is not readily understood during explaining 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 5 of the invention.
Fig. 5 is the sectional view schematic diagram of the first guide rail 12 of the invention.
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 it present.The structure content being previously mentioned in following examples, it is attached with specification
Figure is reference.
Each exemplary embodiment of the present invention is described below with reference to accompanying drawings.
Embodiment one, the present invention convert apparatus for demonstrating, including housing 1 for a kind of trigonometric function image, are placed with housing 1
Telescopically adjustable demonstration cloth 2, the demonstration upper and lower side of cloth 2 are distributed with more first silk threads 3, the first silk thread 3 be it is elastic, outside
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 both 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 forms 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
Two apertures 801, fixing axle 10 is fixed with support frame 9, line wheel 11 is installed, line wheel 11 can be around fixing axle 10 in 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 rotates
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 are individually positioned in the left and right ends of housing 1, and the second guide rail 12 can slide 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 slide along the second guide rail 13, and the second sliding block 13 is with drilling
Show and be connected with more second silk threads 14 between cloth 2.
Embodiment two, on the basis of embodiment one, flat board 15 is installed in described housing 1, flat board 15, which is placed on, drills
Show the rear of cloth 2, flat board 15 encloses one block of dismountable plate, and changeless SIN function y=Sin x is shown on flat board 15
Curve, two graduated scales 16 are installed in housing 1, two graduated scales 16 are mutually perpendicular to place, and graduated scale 16 is placed on demonstration cloth 2
Between flat board 15, graduated scale 16 can slide along housing 1.
Embodiment three, on the basis of embodiment two, the sine that y=Sin x is shown on described demonstration cloth 2 is bent
Line.
Example IV, the present invention are a kind of method realized trigonometric function image and convert apparatus for demonstrating, it is characterised in that bag
Include following steps：The first step, adjustment demonstration cloth 2, make the curve on demonstration cloth 2 and sine curve y=Sin x weights on flat board 15
Close；Second step, zeroing, the starting point for the curve adjusted is overlapped with the zero point on graduated scale 16, graduated scale 16 is fixed；3rd
Step, line wheel 11 is rotated, 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, demonstrate sine curve on cloth 2 and y=A Sin x are become by y=Sin x；4th step, the second guide rail 12 is moved left and right, the
The second sliding block 13 in two guide rails 12 demonstrates cloth 2 by the second silk thread 14 come cross directional stretch, demonstrate sine curve on cloth 2 by y=
A Sin x become y=A Sin ω x；5th step, the axis of guide 4 is pulled, make 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, pure between affairs to establish
Pure relation, that is, function model, trigonometric function is one of six class basic elementary functions in function, therefore, in education and instruction
Link, trigonometric function are regarded as the difficult point and emphasis of examination, and teacher can explain the conversion process of trigonometric function and trigonometric function emphatically,
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 the frame of a rectangle, and the inner side of housing 1 is provided with the groove slided for two graduated scales 16, two graduated scales 16
Difference can be slided along the level of housing 1 and vertical sliding, staggers 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, demonstrates the curve that y=Sin x is shown on 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 demonstrate the flexible of cloth 2 with this to realize.
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 slide 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 and the second guide rail 5 are fixed, demonstrate cloth 2
The length of horizontal direction also just secures, and when unclamping housing screw, 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 rotate by demonstration cloth 2, the first aperture 8, second orifice 801 and line wheel 11, line wheel 11 successively, by the
One silk thread 3 is coiled up, and the first silk thread 3 affects demonstration cloth 2 to do longitudinal stretch.
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 more second silk threads 14 act on flexible or translation also occurs.
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 the flat board of one piece 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 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
It can adsorb on the wall or desk, convenience operate.
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, places because unbalance stress causes demonstration cloth 2 uncontrollable unexpected deformation occur, influences 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 provided by the invention, effectively solve trigonometric function graph
As conversion explanation during static map it is not readily understood the problem of, 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, which is wasted in, makes specific Dynamic Graph.
It will be noted that although 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 technical characteristics in embodiment to solve specific technical problem may it is not necessary to, so as to not no 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 appropriate with the feature, key element and/or function of other one or more embodiments mutual group
Conjunction, combination or cooperation, unless the combination, combination or cooperation can not substantially be implemented.
Claims (4)
1. a kind of trigonometric function image converts apparatus for demonstrating, it is characterised in that including housing（1）, housing（1）It is interior be provided with it is scalable
The demonstration cloth of regulation（2）, demonstrate cloth（2）More the first silk threads with elasticity are distributed with upper and lower side（3）, housing（1）Upper end is with
End is respectively equipped with an axis of guide（4）, the axis of guide（4）Both ends are placed in housing（1）Outside, housing（1）Distinguish top and bottom
Provided with the first guide rail（5）, the first guide rail（5）It is interior be provided with it is 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）It is provided with front and rear the first aperture communicated（8）, housing（1）Back is fixedly mounted
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 of left and right ends（12）, second
Guide rail（12）For can be along the axis of guide（4）The structure of slip, the second guide rail（12）It is interior to be provided with multiple second sliding blocks（13）, the second sliding block
（13）With demonstrating cloth（2）Between be connected with more second silk threads（14）.
A kind of 2. trigonometric function image conversion apparatus for demonstrating according to claim 1, it is characterised in that described housing
（1）Interior be provided with 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）Interior be provided with 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.
A kind of 3. trigonometric function image conversion apparatus for demonstrating according to claim 2, it is characterised in that described demonstration cloth
（2）On show y=Sin x sine curve.
A kind of a kind of 4. method for the trigonometric function image conversion apparatus for demonstrating realized described in claim 2, it is characterised in that bag
Include 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 are overlapped；
Second step, zeroing, by the starting point and graduated scale of the curve adjusted（16）On zero point overlap, by graduated scale（16）Gu
It is fixed；
3rd step, rotate 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, demonstrate cloth（2）Upper sine curve becomes y=A Sin x by y=Sin x；
4th step, move left and right the second guide rail（12）, the second guide rail（12）The second interior sliding block（13）Pass through 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, pull 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 and move 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 CN106898200A (en) | 2017-06-27 |
| CN106898200B true CN106898200B (en) | 2017-12-08 |
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| Application Number | Title | Priority Date | Filing Date |
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| 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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| 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 | 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 |
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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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