Trigonometric Function Quick Reference Chart

Abstract

This provides a visually easy-to-understand quick reference chart to help beginners learn trigonometry without getting stuck. [Solution] The device is composed of two sheets, an upper and an lower sheet. The upper sheet 20 is rotatably fixed to the lower sheet 10. On the upper surface of the lower sheet, a circle of a predetermined radius is drawn around the axis, and on this circle, with θ being in radians, at positions θ = 0, π / 6, π / 4, π / 3, π / 2, 2π / 3, 3π / 4, 5π / 6, π, 7π / 6, 5π / 4, 4π / 3, 3π / 2, 5π / 3, 7π / 4, 11π / 6, a scale and the numbers 0, 1, 2, 3, 4, 3, 2, 1 are drawn in that order. The upper sheet 20 is transparent and has a first mark 21 indicating a position of radial length from the axis, and a second mark 22 indicating a number at a position rotated by π / 2 with respect to the line connecting the axis to the first mark, allowing the calculation of trigonometric function values ​​to be observed.

Description

Technical Field

[0001] The present invention relates to a trigonometric function quick reference table that can easily grasp the values of trigonometric functions of θ = 0, π / 6, π / 4, π / 3, π / 2, 2π / 3, 3π / 4, 5π / 6, π, 7π / 6, 5π / 4, 4π / 3, 3π / 2, 5π / 3, 7π / 4, 11π / 6, where θ is in radians.

Background Art

[0002] When learning trigonometric functions in high school or the like, three functions, sin, cos, and tan, appear. The angles that were previously taught as 360° for one rotation are expressed using the irrational number π as radians. And for some angles, it is necessary to memorize the values of trigonometric functions, which poses a problem that it is easy to get confused and bewildered for those who are learning for the first time.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] The present invention has been made in view of the above, and aims to provide a quick reference table that is visually easy to understand when learning trigonometric functions for the first time, so that one can acquire trigonometric functions without getting stuck.

Means for Solving the Problems

[0005] The trigonometric function quick reference table described in claim 1 is composed of two sheets, an upper and an lower sheet, the upper sheet being rotatably fixed to the lower sheet, the upper surface of the lower sheet having a circle of a predetermined radius centered on the axis, and markings and the numbers 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1 drawn on the circle at positions where θ is in radians, θ = 0, π / 6, π / 4, π / 3, π / 2, 2π / 3, 3π / 4, 5π / 6, π, 7π / 6, 5π / 4, 4π / 3, 3π / 2, 5π / 3, 7π / 4, 11π / 6 respectively, the upper sheet being transparent, and half of the sheet being visible from the axis. The device is characterized by comprising a first mark indicating the position of the diameter length, and a second mark indicating a number at a position rotated by π / 2 with respect to the line connecting the axis to the first mark, and by aligning the first mark with any of the scales, it can be seen that the values ​​of the trigonometric functions at that position can be calculated using the number A on that scale and the number B indicated by the second mark as sinθ=sqrt(A) / 2, cosθ=sqrt(B) / 2, tanθ=sqrt(A) / sqrt(B), (wherein if the mark is in the range π < θ < 2π, a minus sign is added to the square root related to that mark).

[0006] The invention described in claim 2 is characterized in that, in the trigonometric function quick reference table described in claim 1, the first mark is a straight line representing the radius length, and the second mark is a frame surrounding the number.

[0007] The invention described in claim 3 is characterized in that, in the trigonometric function quick reference table described in claim 2, the numbers at the positions of 7π / 6, 5π / 4, 4π / 3, 3π / 2, 5π / 3, 7π / 4, and 11π / 6 are drawn in a different color from the numbers at the positions of θ=0, π / 6, π / 4, π / 3, π / 2, 2π / 3, 3π / 4, 5π / 6, and π, and further, on the upper surface of the lower sheet, the same or equivalent notation is made using a - mark representing the straight line and a □ mark representing the frame, such that sinθ=sqrt(-) / 2, cosθ=sqrt(□) / 2, tanθ=sqrt(-) / sqrt(□), and when the mark surrounds the numbers of the different color, a minus sign is added to the square root related to the mark. [Effects of the Invention]

[0008] According to this invention, when learning trigonometric functions for the first time, a visually easy-to-understand quick reference chart can be provided, enabling learners to master trigonometric functions without encountering difficulties. [Brief explanation of the drawing]

[0009] [Figure 1] This is an example of how a quick reference chart can be structured. [Figure 2] This is a diagram showing the values ​​of the trigonometric function θ = π / 6. [Figure 3] This is a diagram showing the values ​​of the trigonometric function θ = 3π / 4. [Figure 4] This is a diagram showing the values ​​of the trigonometric function θ = 4π / 3. [Modes for carrying out the invention]

[0010] The embodiments of this invention will be described in detail below with reference to the drawings. Hereafter, the trigonometric function quick reference table will be referred to simply as the quick reference table as appropriate. Figure 1 is an explanatory diagram showing an example of the configuration of the quick reference chart of the present invention. Reference sheet 1 consists of a roughly square lower sheet 10 and a disc-shaped transparent upper sheet 20. The upper sheet 20 is rotatably attached to the lower sheet 10 by a hollow rivet 11 in the center of the disc. In addition, a hole 12 is made by an eyelet in one corner of the lower sheet 10, allowing for string to be threaded through as needed. Additionally, the lower sheet 10 has a circle 15 and a radius 16 drawn on it. In addition, starting from the edge of the radius 16, along the circumference, with θ being in radians, at positions θ = 0, π / 6, π / 4, π / 3, π / 2, 2π / 3, 3π / 4, 5π / 6, π, 7π / 6, 5π / 4, 4π / 3, 3π / 2, 5π / 3, 7π / 4, 11π / 6, scale 18 and the numbers 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1 are drawn (these numbers will be referred to as the number N). Of these, the numbers at θ=0,π / 6,π / 4,π / 3,π / 2,2π / 3,3π / 4,5π / 6, and π are shown in black, while the numbers at θ=7π / 6,5π / 4,4π / 3,3π / 2,5π / 3,7π / 4, and11π / 6 are shown in red (Note that in Figure 1, for the sake of explanation, the numbers are shown in italics instead of red).

[0011] Furthermore, the following formula and comments are attached to the lower sheet 10.

number

[0012] The upper sheet 20 is a transparent sheet on which a straight line 21 with a radius length extending from the hollow rivet 11 portion and a surrounding frame 22 enclosing the number N located π / 4 away from the straight line 21 centered on the hollow rivet 11 are drawn.

[0013] <How to use> Use Quick Reference Chart 1 as follows: First, rotate the top sheet 20 to align the line 21 with the scale 18 at the angle θ of the trigonometric function you want to know. Let the number N at this point be number A. At this time, enclose the number N with the surrounding frame 22. Let the enclosed number N be number B. Then, as shown in sheet 10 below, sinθ = sqrt(A) / 2 cosθ = sqrt(B) / 2 tanθ = sqrt(A) / sqrt(B) This is the result.

[0014] Specifically, for example, when θ = π / 6, A = 1 and B = 3, and indeed sinθ = √1 / 2 cosθ = √3 / 2 tanθ = √1 / √3 This is the case (see Fig. 2).

[0015] Similarly, when θ = 3π / 4, A = 2, B = 2 (in red), and indeed sinθ = √2 / 2 cosθ = -√2 / 2 tanθ = √2 / (-√2) = -1 This is the case (see Fig. 3).

[0016] Also, when θ = 4π / 3, A = 3 (in red), B = 1 (in red), and indeed sinθ = -√3 / 2 cosθ = -√1 / 2 tanθ = -√3 / (-√1) = √3 This is the case (see Fig. 4).

Industrial Applicability

[0017] According to the present invention, for the first time, trigonometric functions that are newly learned can be visually and sensuously acquired, and after a while, the values of trigonometric functions of a predetermined angle can be stated without a quick reference table.

Explanation of Signs

[0018] 1 Quick reference table 10 Lower sheet 11 Hollow rivet 12 Hole 15 Circle 16 Radius 18 Scale 20 Upper sheet 21 Straight line 22 Enclosing frame

Claims

1. It is composed of two sheets, one above the other. The upper sheet is rotatably fixed to the lower sheet, On the upper surface of the lower sheet, a circle with a predetermined radius centered on the axis is drawn, and on this circle, with θ being in radians, at positions θ = 0, π / 6, π / 4, π / 3, π / 2, 2π / 3, 3π / 4, 5π / 6, π, 7π / 6, 5π / 4, 4π / 3, 3π / 2, 5π / 3, 7π / 4, 11π / 6, a scale and the numbers 0, 1, 2, 3, 4, 3, 2, 1 are drawn in that order. The upper sheet is transparent and has a first mark indicating a position of radial length from the axis, and a second mark indicating a number at a position π / 2 rotations with respect to the line connecting the axis and the first mark. It is equipped with, When the first mark is aligned with any of the scales, the value of the trigonometric function at that position is calculated using the number A on that scale and the number B indicated by the second mark. sinθ = sqrt(A) / 2, cosθ = sqrt(B) / 2, tanθ = sqrt(A) / sqrt(B), (however, when the symbol is in the range π < θ < 2π, a minus sign is placed on the square root related to that symbol.) A trigonometric function quick reference table characterized by its ability to show how the calculations are performed.

2. The trigonometric function quick reference table according to claim 1, characterized in that the first mark is a straight line of radius length, and the second mark is a frame surrounding a number.

3. The numbers at positions 7π / 6, 5π / 4, 4π / 3, 3π / 2, 5π / 3, 7π / 4, and 11π / 6 are drawn in a different color than the numbers at positions θ=0, π / 6, π / 4, π / 3, π / 2, 2π / 3, 3π / 4, 5π / 6, and π. On the upper surface of the lower sheet, a - mark representing the straight line and a □ mark representing the frame are used, The trigonometric function quick reference table according to claim 2, characterized in that it has the same or equivalent notation as sinθ = sqrt(-) / 2, cosθ = sqrt(□) / 2, tanθ = sqrt(-) / sqrt(□), and when a mark surrounds a number of a different color, a minus sign is added to the square root related to that mark.

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