CN210324743U

CN210324743U - Tool for measuring trigonometric function

Info

Publication number: CN210324743U
Application number: CN201921363734.0U
Authority: CN
Inventors: 黄小华
Original assignee: Individual
Current assignee: Individual
Priority date: 2019-08-21
Filing date: 2019-08-21
Publication date: 2020-04-14
Anticipated expiration: 2029-08-21

Abstract

The utility model discloses a measure instrument of trigonometric function, including parts such as main scale, first vice chi, the vice chi of second, rotation cotter, scale mark, graduated scale, scale mark, tongue and recess. The utility model discloses the main points lie in nimble design on the main scale and have the graduated scale, can adjust corresponding angle through the effect flexibility of rotating the cotter, make its nimble removal in "U" shape groove on the main and auxiliary chi in addition, and read out the scale interval of using through the scale mark on the main and auxiliary chi, can calculate the trigonometric function value of corresponding angle according to numerical value, help the student directly perceived image understand trigonometric function with poor formula, multiple angle formula and half angle formula, accelerate student's understanding speed and memory efficiency, promote teaching efficiency and quality.

Description

Tool for measuring trigonometric function

Technical Field

The utility model relates to a mathematical education tool equipment field especially relates to a measure instrument of trigonometric function.

Background

Trigonometric functions are functions in mathematics that fall within the transcendental function of elementary functions. Their nature is the mapping between the variables of any set of angles and a set of ratios. A typical trigonometric function is defined in a planar rectangular coordinate system. Its domain is defined as the entire real number domain. The trigonometric function has certain difficulty for a learner, the derivation process and recitation trigonometric function formula of the trigonometric function need to be mastered, some difficulty is brought to teacher teaching, how to help students understand and remember is critical, and the teaching mode adopted by the teacher at present is generally blackboard writing demonstration and multimedia information technology dynamic display teaching students. Students can only accept the derivation of related formulas through the visual sense and self-comprehension ability at that time, and the students can perceive the formulas singly in a short time, are difficult to understand and easy to forget, so that the students are not favorable for flexibly mastering trigonometric function formulas.

Therefore, how to design a tool for measuring the trigonometric function can visually and vividly measure and calculate the value of any trigonometric function, and help students visually and vividly understand the sum and difference formula, the multiple angle formula and the half angle formula of the trigonometric function. Is a problem to be solved in the industry.

SUMMERY OF THE UTILITY MODEL

In order to solve the defects of the prior art, the utility model provides a tool for measuring trigonometric function, which comprises a main ruler, wherein a first auxiliary ruler is arranged at the head end of the main ruler, a second auxiliary ruler is vertically arranged at the rear end of the main ruler, and the main ruler and the first auxiliary ruler are connected through a rotating pin; the main scale comprises a graduated scale, a graduated line marked on the center line of the graduated scale, a main scale movable hole arranged at the position of the graduated line '0', a graduated scale arranged at the upper part of the head end of the graduated scale, a graduated line carved on the graduated scale, and convex grooves arranged at the upper and lower positions of the tail end of the graduated scale; the graduated scale is an graduated semicircle with the radius of 5 cm, and the circle center of the graduated semicircle is superposed with the 0 scale of the graduated scale; the minimum unit value of the scale on the graduation line is 1 degree, and the scale line of 0 degree is superposed with the scale line; the first auxiliary scale comprises a first auxiliary scale graduation line arranged on the central line and a first auxiliary scale movable hole arranged at the '0' graduation position on the first auxiliary scale graduation line; the second auxiliary scale comprises a second auxiliary scale graduation line arranged on the central line and grooves arranged above and below the end part of the second auxiliary scale, and the graduation line '0' of the second auxiliary scale graduation line is overlapped with the graduation line on the graduated scale; the center line of the main ruler is perpendicular to the center line of the second auxiliary ruler.

Preferably, the main ruler, the first auxiliary ruler and the second auxiliary ruler are all 30 cm in length and 4 cm in width.

Preferably, the smallest scale unit on the scale mark, the first sub scale mark and the second sub scale mark is 0.1 cm; 5 cm of blank rulers are reserved at the front ends of the scale marks and the 0 scale mark of the first auxiliary ruler; and a blank ruler with the length of 2 centimeters is reserved at the front end of the scale mark of 0 of the second auxiliary ruler.

Preferably, the shape of the convex groove and the shape of the concave groove are both U-shaped, and the convex groove and the concave groove are matched and connected in a sliding manner; the length of the convex groove is 15 cm, and the length of the groove is 4 cm.

Preferably, the main scale movable hole and the first auxiliary scale movable hole have the same aperture and are matched and rotatably connected with the rotating pin bolt.

The utility model discloses a design point lies in that nimble design has the graduated scale on the main scale, can adjust corresponding angle through the effect flexibility of rotating the cotter, make its nimble removal in "U" shape groove on the main and auxiliary chi in addition, and read out the scale interval of using through the scale mark on the main and auxiliary chi, can calculate the trigonometric function value of corresponding angle according to numerical value, help the student directly perceived image understand trigonometric function with poor formula, multiple angle formula and half angle formula for student's understanding speed and memory efficiency promote teaching efficiency and quality.

Compared with the prior art, the utility model discloses lie in adopting the major-minor chi that the student can the direct operation, audio-visual vivid measurement calculates the value of arbitrary trigonometric function, and help the student audio-visual vivid understand trigonometric function's sum difference formula, multiple angle formula and half angle formula. The understanding speed and the memory efficiency of students are accelerated, and the teaching efficiency and the teaching quality are improved.

Drawings

Fig. 1 is a schematic view of the overall structure of the present invention.

Fig. 2 is a schematic structural view of the main scale of the present invention.

Fig. 3 is a schematic structural view of the first auxiliary ruler of the present invention.

Fig. 4 is a schematic structural view of a second auxiliary ruler of the present invention.

Fig. 5 is a schematic diagram of formula derivation according to the present invention.

Detailed Description

The following detailed description of the present invention will be made with reference to the accompanying drawings and examples.

As shown in fig. 1 to 5, the utility model provides a tool for measuring trigonometric function, which comprises a main ruler 1, wherein a first auxiliary ruler 2 is arranged at the head end of the main ruler 1, a second auxiliary ruler 3 is vertically arranged at the rear end of the main ruler 1, and the main ruler 1 is connected with the first auxiliary ruler 2 through a rotating pin 4; the main scale 1 comprises a graduated scale 101, a graduation line 102 marked on the central line of the graduated scale 101, a main scale movable hole 103 arranged at the position of the graduation line 102 '0', a graduated scale 104 arranged at the upper part of the head end of the graduated scale 101, a graduation line 105 carved on the graduated scale 104, and a convex groove 106 arranged at the upper and lower positions of the tail end of the graduated scale 101; the graduated scale 104 is an graduated semicircle with the radius of 5 cm, and the circle center of the graduated semicircle is superposed with the scale of 0 of the graduated scale 101; the minimum unit value of the scale on the graduation line 105 is 1 degree, and the scale line of "0" degree is superposed with the scale line 102; the first auxiliary scale 2 comprises a first auxiliary scale graduation line 201 arranged on the central line and a first auxiliary scale movable hole 202 arranged at the graduation position of '0' on the first auxiliary scale graduation line 201; the second sub ruler 3 comprises a second sub ruler scale mark 301 arranged on the central line and grooves 302 arranged above and below the end part of the second sub ruler, and the scale mark 301 '0' of the second sub ruler coincides with the scale mark 102 on the scale 101; the central line of the main ruler 1 is perpendicular to the central line of the second auxiliary ruler 3.

The main ruler 1, the first auxiliary ruler 2 and the second auxiliary ruler 3 are all 30 cm in length and 4 cm in width; the minimum scale unit on the scale mark 102, the first sub-scale mark 201 and the second sub-scale mark 301 is 0.1 cm; 5 cm of blank rulers are reserved at the front ends of the scale marks 102 and the scale mark 201 '0' of the first auxiliary ruler; a blank ruler with the length of 2 cm is left at the front end of the scale line 301 '0' of the second auxiliary ruler. The reserved length is matched and corresponding, so that the reading operation is convenient; the shape of the convex groove 106 and the shape of the concave groove 302 are both U-shaped, the convex groove 106 and the concave groove 302 are in matched sliding connection, the length of the convex groove 106 is 15 cm, the length of the concave groove 302 is 4 cm, and the second auxiliary ruler can conveniently slide on the main ruler. The main scale movable hole 103 and the first auxiliary scale movable hole 202 have the same aperture and are matched with the rotating pin bolt 4 to be rotatably connected, so that the main scale and the first auxiliary scale can be flexibly rotated conveniently.

When the tool is used, the first auxiliary scale 2 is rotated under the action of the rotating pin 4, the angle to be measured is adjusted through the graduated scale 104 on the main scale 1, the corresponding angle is read through the graduated line 105, the second auxiliary scale 3 moves on the main scale 1 through the matching of the convex groove 106 and the concave groove 302, and finally the numerical values corresponding to the three sides are read through the scale marks on the main scale 1, the first auxiliary scale 2 and the second auxiliary scale 3. The method can visually and vividly measure and calculate the value of any trigonometric function, and help students visually and vividly understand the sum and difference formula, the multiple angle formula and the half angle formula of the trigonometric function.

Tools may be utilized to aid in understanding the derivation of trigonometric functions and difference formulas,

for example, cos (α + β) = cos α. cos β -sin α. sin β

Let α be an acute angle, make a circle with QO radius of 1, and point A, B be on QO;

and the included angle between OA and the X axis is α;

the included angle between OB and the X axis is β;

making a symmetrical point A' of the point A about the X axis;

∠ a' OB = α + β;

from title a (cos α, sin α);

B（cosβ，sinβ）；

A’（cosα，-sinα）

therefore, OA' = OA = OB =1

From the law of cosines to obtain A' B²=OA’²+OB²-2OA’·OB·cos(α+β)；

Namely A' B²=2-2cos(α+β)

From the distance between two points:

A’B²=（cosα-cosβ）²+（-sinα-sinβ）²；

namely A' B²=2-2 cosα·cosβ+2sinα·sinβ；

So cos (α + β) = cos α · cos β -sin α · sin β;

because sin (α + β) = cos [ pi/2- (α + β) ] = cos [ pi/2- α) + β ];

sin (α + β) = cos (pi/2- α) cos β + sin (pi/2- α) sin β;

sin (α + β) = sin α cos β + cos α sin β;

let α = β;

sin2 α =2sin α cos α

The above embodiments only represent some embodiments of the present invention, and the description thereof is specific and detailed, but not to be construed as limiting the scope of the present invention. It should be noted that, for those skilled in the art, without departing from the spirit of the present invention, several variations and modifications can be made, which are within the scope of the present invention. Therefore, the appended claims should be accorded the full scope of protection and protection to the present invention.

Claims

1. A tool for measuring trigonometric functions, characterized by: the multifunctional ruler comprises a main ruler (1), wherein a first auxiliary ruler (2) is arranged at the head end of the main ruler (1), a second auxiliary ruler (3) is vertically arranged at the rear end of the main ruler (1), and the main ruler (1) is connected with the first auxiliary ruler (2) through a rotating pin bolt (4); the main scale (1) comprises a graduated scale (101), a graduated line (102) marked on the central line of the graduated scale (101), a main scale movable hole (103) arranged at the position of 0 of the graduated line (102), a graduated scale (104) arranged at the upper part of the head end of the graduated scale (101), a graduated line (105) carved on the graduated scale (104), and a convex groove (106) arranged at the upper and lower positions of the tail end of the graduated scale (101); the graduated scale (104) is an graduated semicircle with the radius of 5 cm, and the circle center of the graduated semicircle is superposed with the 0 scale of the graduated scale (101); the minimum unit value of the scale on the graduation line (105) is 1 degree, and the scale line of 0 degree is superposed with the scale line (102); the first auxiliary scale (2) comprises a first auxiliary scale graduation line (201) arranged on the central line and a first auxiliary scale movable hole (202) arranged at the '0' graduation position on the first auxiliary scale graduation line (201); the second auxiliary scale (3) comprises a second auxiliary scale graduation line (301) arranged on the central line and grooves (302) arranged above and below the end part of the second auxiliary scale, and the graduation line (301) '0' of the second auxiliary scale graduation line is overlapped with the graduation line (102) on the graduated scale (101); the central line of the main ruler (1) is vertical to the central line of the second auxiliary ruler (3).

2. The tool for measuring trigonometric functions of claim 1, wherein: the main ruler (1), the first auxiliary ruler (2) and the second auxiliary ruler (3) are all 30 cm in length and 4 cm in width.

3. The tool for measuring trigonometric functions of claim 1, wherein: the minimum scale unit on the scale mark (102), the first auxiliary scale mark (201) and the second auxiliary scale mark (301) is 0.1 cm; 5 cm of blank rulers are reserved at the front ends of the scale marks (102) and the scale marks (201) '0' of the first auxiliary ruler; and a blank ruler with the length of 2 cm is reserved at the front end of the scale mark (301) '0' of the second auxiliary ruler.

4. The tool for measuring trigonometric functions of claim 1, wherein: the convex groove (106) and the concave groove (302) are both U-shaped and are matched and slidably connected; the length of the convex groove (106) is 15 cm, and the length of the concave groove (302) is 4 cm.

5. The tool for measuring trigonometric functions of claim 1, wherein: the main scale movable hole (103) and the first auxiliary scale movable hole (202) are the same in aperture and are in matched rotary connection with the rotary pin bolt (4).