KR100686795B1 - Trigonometric ratio rule - Google Patents

Abstract

A trigonometric ratio rule is provided to measure trigonometric ratios like sine, cosine, and tangent values for all angles with measuring the angle and to facilitate carrying by making the rule of transparent plates in a semi-circle or circle form. The trigonometric ratio rule is composed of a first standardized circle(1) having a radius that is 1; horizontal and vertical lines(2,3) branched from the center of the first circle across each other; horizontal and vertical scale lines formed at regular intervals in parallel to the horizontal and vertical lines in the first circle; horizontal and vertical scale values marked along the horizontal and vertical lines from the center of the first circle; a second circle concentric with the first circle, the radius bigger than 1, and angle scales and angle values marked in a counterclockwise direction; and a third circle concentric with the first circle and reduced at the predetermined ratio. All components of the trigonometric ratio rule are formed on a transparent plate.

Description

Trigonometric ratio rule

1 is a plan view of a semi-circular triangular visa according to an embodiment of the present invention.

2 is a plan view of a circular triangular visa according to an embodiment of the present invention.

3 is a view for explaining a process of measuring a triangular ratio using the triangular visa of FIG.

<Description of main parts of drawing>

ABC ... any right triangle

ADE ... Right triangle that standardizes hypotenuse length of arbitrary right triangle in one unit

AFG ... Reduces the base length of any right triangle to 1/10 standardized right triangle

1 ... A circle with a radius of 1 unit that normalizes the hypotenuse of all right triangles

2 ... Horizontal line diverged bidirectionally from the center of the normalized circle (x-axis of the Cartesian coordinate)

3 ... Vertical line branched bidirectionally from the center of the normalized circle (y-axis of the plane Cartesian coordinate)

4 ... Circumference showing the angle counterclockwise from the horizontal line on the right through the center of the standardized circle

5 ... Circumference showing the angle counterclockwise from the left horizontal line through the center of the standardized circle

6 ... y-axis coordinates of normalized right triangle ADE height

7 ... x-axis coordinates of base of normalized right triangle ADE

8a, 8b ... Two vertical lines parallel to the y-axis at points one tenth the radius of the normalized circle

9 ... y-axis coordinates of the hypotenuse of a normalized right triangle and the point where they meet a vertical line parallel to the y-axis at a point one tenth of the radius in the + x-axis direction.

10 ... The sign of the triangle ratio in the quadrant

11. A small circle whose radius is one tenth the radius of the normalized circle.

The present invention relates to a tool that can directly measure the triangular ratio, and more particularly, a simple measuring tool that can directly measure the sine, cosine and tangent values according to the angle while measuring the angle (hereinafter referred to as 'triangle visa'). ').

In general, the triangular ratio is a special angle that can be easily obtained by the geometric method of 30 degrees, 45 degrees, and 60 degrees, and a right triangle is formed on an equilateral triangle having a length of 2 and a square having a length of 1 side. Find the height or length of the hypotenuse and then calculate the triangles by calculation.

For non-special angles, use a trigonometric function, use a previously calculated triangular ratio table, or construct a circle of radius length 1 on the xy coordinates of the Cartesian plane coordinates on the grid to obtain a triangular ratio for any angle. Or have to use a calculator to find the triangle ratio.

As such, although mankind has been using triangle ratios since ancient Egyptian times, no instrument has been created that can measure angles and measure triangle ratios directly.

The present invention can directly measure the triangular ratio at the same time measuring the angle for all angles, and seeks an easy-to-use tool such as a protractor made of a semi-circular and circular transparent plate that is generally used for measuring angles at present. In order to obtain the triangular ratio, the triangular ratio for the general angle can be obtained by direct measurement without the inconvenience of conventional methods such as drawing on a grid paper or using a trigonometric table or a calculator. The purpose of this course is to provide a triangular ratio measurement tool (hereinafter referred to as 'triangle visa') that makes it easy to acquire the concept of triangular ratio in the process.

Triangular visa according to an aspect of the present invention for achieving the above technical problem, the first circle of the standardized radius of the transparent plate; Horizontal lines and vertical lines branched to be orthogonal to each other from the center of the first circle; Horizontal and vertical grid lines at equal intervals parallel to the horizontal and vertical lines, respectively, in the first circle; Horizontal and vertical scale values respectively displayed along horizontal and vertical lines from the center of the first circle; A second circle concentric with the first circle and having a radius greater than 1 and an angular scale and an angular value displayed in a counterclockwise direction; And a third circle concentric with the first circle and reduced at a predetermined magnification.

Triangular visa according to another aspect of the present invention for achieving the above technical problem, the first semicircle of the standardized radius of the transparent plate; Horizontal lines and vertical lines branched to be perpendicular to each other from the center of the first semicircle; Horizontal and vertical grid lines at equal intervals parallel to the horizontal and vertical lines, respectively, in the first semicircle; A horizontal scale value and a vertical scale value respectively displayed along a horizontal line and a vertical line from the center of the first semicircle; A second semicircle which is concentric with the first semicircle and whose radius is greater than 1 and whose angular scale and angle value are counterclockwise; And a third semicircle concentric with the first semicircle and reduced at a predetermined magnification.

In the present invention, the horizontal grid line and the vertical grid line may be formed of a solid line in which a predetermined number of colors are periodically repeated.

Preferably, the third circle (semi-circle) is a triangular ratio measuring tool, characterized in that 1/10 times reduced on the basis of the first circle (semi-circle).

Preferably, the transparent plate further includes a solid line branched in the vertical direction with the branched horizontal line from a point where the horizontal line branched from the center of the first circle (semicircle) and the third circle (semicircle) meet.

Preferably, in the transparent plate, the sign of the sine, cosine and tangent values according to the angular range of the quadrant divided by a horizontal line and a vertical line branched from the center of the first circle (semicircle) is further at a predetermined position of the quadrant. Is indicated.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, terms or words used in the present specification and claims should not be construed as being limited to the common or dictionary meanings, and the inventors should properly explain the concept of terms in order to best explain their own invention. Based on the principle that can be defined, it should be interpreted as meaning and concept corresponding to the technical idea of the present invention. Therefore, the embodiments described in the specification and the drawings shown in the drawings are only the most preferred embodiment of the present invention and do not represent all of the technical idea of the present invention, various modifications that can be replaced at the time of the present application It should be understood that there may be equivalents and variations.

1 is a plan view of a semi-circular triangular visa according to an embodiment of the present invention, Figure 2 is a plan view of a circular triangular visa according to an embodiment of the present invention, Figure 3 is a process for obtaining a triangular ratio using the triangular visa of FIG. It is a figure for explanation.

All right triangles can be represented in one standardized circle (1). That is, as shown in FIG. 3, the horizontal line 2 and the vertical line 3 are drawn at the center of the standardized circle, and the vertex A of each BAC of any general right triangle ABC is aligned with the center of the standardized circle, and the base BC is normalized. When the hypotenuse is standardized by 1 unit with the radius of the standardized circle while matching the horizontal line passing from the center of the circle, a standardized right triangle ABC is formed, which is similar to the general right triangle ABC. At this time, the line segment AE, which is the base of the normalized right triangle ADE, may be represented on the horizontal line, and the line segment DE, which is the height thereof, may be represented on the vertical line parallel to the vertical line 3 passing through the center of the standardized circle.

Draw a circle that is slightly larger than the radius of the standardized circle and is concentric with the standardized circle, and displays the angle of dividing 360 degrees 720 degrees along the circumference in the counterclockwise direction at 0.5 degree intervals based on the horizontal line on the right side (2) passing through the center of the circle. The angle of the angle between the base and the oblique plane of the lower surface (4), the general right triangle ABC and the normalized right triangle ADE can be measured. In order to measure the angle more precisely, the radius of the standardized circle can be increased, and the circumference can be divided into 3600 equal parts and 7200 equal parts, and the angles can be displayed at 0.1 degree and 0.05 degree intervals.

To improve the ease of measurement of the ratio, set the center of the standardized circle as the origin and set the horizontal line in the 0 degree direction to the + x axis and the horizontal line in the 180 degree direction to the -x axis (2). The orthogonal plane (x, y) coordinates of the + y axis and the 270 degree direction with the -y axis (3) are divided into quadrants of four areas, and the height of the standardized right triangle ADE is the coordinate of the y axis (6). The length of the bottom side is represented by the coordinate (7) of the x-axis.

For an angle consisting of the hypotenuse and the base of the right triangle, the sin value, the ratio of the length of the hypotenuse and the height, and the cosine value, the ratio of the length of the hypotenuse and the height, are equal to the ratio of the length of the radius and the height of the standardized circle. It can be expressed as the ratio of the radius to the length of the base. To this end, in order to directly measure the triangular ratio in the present invention, the radius of the normalized circle, which is the length of the normalized hypotenuse, is set to 1, and the scale of 10 equals, 100 equals, 1000 equals, and 10000 equals is divided into x-axis coordinates (2). If the numerical values corresponding to equal parts between 0 and 1 are sequentially given by the coordinates (3) and the y-axis coordinates (3), the sine of the triangular ratios of the standardized right triangle ADE is the length of the height of the standardized right triangle ADE shown on the y axis. The numerical value (6) of the y-axis coordinate coinciding with DE and the cosine value are the numerical value (7) of the x-axis coordinate corresponding to the length AE of the base of the normalized right triangle ADE.

The tangent value, which is the ratio of the length of the base of the right triangle to the triangular ratio, is obtained from the center of the standardization circle at the point of one-tenth the radius of the standardization circle in the + x and -x directions from the center of the standardization circle. Drawing two vertical lines (8a, 8b) parallel to the y-axis, respectively, forms a right-angled triangle AFG, which is a tenth similarity to a normalized right-angled triangle, which is the length of the base of the normal triangle ABC. It is a right triangle standardized to one tenth of the radius of. The ratio of the length of the base segment AG, which is the tangent of the formed right triangle AFG, and the height of the line segment FG, which is the tangent of the formed right triangle AFG, is in the direction of the hypotenuse and + x axis of the normalized right triangle. The value of the y-axis coordinate 9 at the point where it meets the vertical line 8a parallel to the y-axis at a point equal to tenth of the radius is multiplied by 10.

In order to increase the utilization of the triangular visa of the present invention, a larger circle is drawn by drawing an angle rotated 180 degrees with respect to the angle (4) already displayed, that is, an angle counterclockwise with respect to the horizontal line on the left passing through the center of the standardized circle. Displayed on the circumference (5) so that the triangular ratio can be measured irrespective of the vertical direction, and as shown in Fig. 1, the circular triangular bizarre is made of a semicircular triangular bisecter divided into two halves along a line connecting 0 and 180 degrees. Like the semi-circular protractor being used, it is possible to measure the angle and at the same time the triangular ratio, and between the two circumferences marked the angle indicates the sign (10) of the triangular ratio in the quadrant.

In the case of the semi-circular triangular visa of FIG. 1, two vertical lines parallel to the y-axis at the point of one-tenth the radius of the normalized circle in the + x-axis direction and the -x-axis direction from the origin of the circle to obtain a tangent value ( 8a, 8b) are extended to the edge of the triangular visa to estimate the tangent values above 10 and below -10.

On the other hand, in the triangular visa of Figs. 1 and 2, a small circle 11, which is one-tenth of the radius of the standardized circle concentric with the standardized circle, is drawn, and a straight line representing an angle of 10 degree intervals from the circumference to the edge of the triangular visa While drawing subsequent line segments, the small circle excludes all line segments representing angles, making it convenient to measure angles and triangle ratios.

Further, in order to facilitate the triangular ratio measurement, various colors can be given to the horizontal lines and the vertical lines that are divided into equal parts of 100 or more. For example, the first line that subdivides 1 unit into 10 equal parts, such as 0.01, 0.021, 0.31, 0.71, etc., is divided into brown, 0.02, 0.022, 0.32, 0.72, etc. The second line is red, the third line is orange, the fourth line is yellow, the fifth line is green, the sixth line is blue, the seventh line is purple, the eighth line is gray, the ninth line is white, the ninth line is white, and the tenth line is black. Color lines representing numerical values can be drawn so that corresponding triangular ratio values can be easily recognized.

As described above, although the present invention has been described by way of limited embodiments and drawings, the present invention is not limited thereto and is intended by those skilled in the art to which the present invention pertains. Of course, various modifications and variations are possible within the scope of equivalents of the claims to be described.

Triangular Visor, the triangular ratio measuring tool of the present invention, can measure the angles of all angles and measure the triangular ratios such as sine values, cosine values, and tangent values for all angles in practical terms. All inconveniences such as drawing on the above can be eliminated, and also in its appearance, it can be manufactured in a semi-circular shape and a circular shape with a transparent plate such as plastic or acrylic, which is very convenient to carry and use.

In the educational aspect of the present invention, it is possible to solve problems using trigonometric ratios only with the concept of similarity ratios that are learned in elementary grades without knowledge of Pythagorean principles or square roots, and learning about trigonometric ratios depends only on plots or triangular ratios. By doing so, the concept of triangular ratio, which was considered only an abstract concept, can be learned as a concrete concept through the actual measurement of triangular ratio, thus leading to education on triangular ratio efficiently. It is expected that learning will be conducted at a lower grade level so that the application of triangular ratios to physics in science education as well as mathematics education can be easily induced.

Claims (9)

A standardized first circle having a radius of 1 on a transparent plate; Horizontal lines and vertical lines branched to be orthogonal to each other from the center of the first circle; Horizontal and vertical grid lines at equal intervals parallel to the horizontal and vertical lines, respectively, in the first circle; Horizontal and vertical scale values respectively displayed along horizontal and vertical lines from the center of the first circle; A second circle concentric with the first circle and having a radius greater than 1 and an angular scale and an angular value displayed in a counterclockwise direction; And a third circle concentric with the first circle and reduced at a predetermined magnification. A standardized first semicircle having a radius of 1 on a transparent plate; Horizontal lines and vertical lines branched to be perpendicular to each other from the center of the first semicircle; Horizontal and vertical grid lines at equal intervals parallel to the horizontal and vertical lines, respectively, in the first semicircle; A horizontal scale value and a vertical scale value respectively displayed along a horizontal line and a vertical line from the center of the first semicircle; A second semicircle which is concentric with the first semicircle and whose radius is greater than 1 and whose angular scale and angle value are counterclockwise; And a third semicircle concentric with the first semicircle and reduced at a predetermined magnification. The method according to claim 1 or 2, The horizontal grid line and the vertical grid line is a triangular ratio measuring tool, characterized in that consisting of a solid line that is periodically repeated a predetermined number of colors. The method of claim 1, The third circle is a triangular ratio measuring tool, characterized in that 1/10 times reduced on the basis of the first circle. The method of claim 2, The third semicircle is a triangular ratio measuring tool, characterized in that 1/10 times reduced on the basis of the first semicircle. The method of claim 1, And the horizontal line branched from the center of the first circle and a solid line branched in a vertical direction from the branched horizontal line from a point where the third circle meets. The method of claim 2, And the horizontal line branched from the center of the first semicircle and a solid line branched in a vertical direction from the branched horizontal line from a point where the third semicircle meets. The method of claim 1, The sign of the sine, cosine and tangent values according to the angular range of the quadrant divided by the horizontal and vertical lines branched from the center of the first circle is further displayed at a predetermined position of the corresponding quadrant. The method of claim 2, The sign of the sine, cosine and tangent value according to the angular range of the quadrant divided by a horizontal line and a vertical line branched from the center of the first semicircle is further displayed at a predetermined position of the corresponding quadrant.

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