The Unit Circle by nnhsmath

Loading the math board and drawing, please wait…

2017-09-17 02:39

This example demonstrates the unit circle, a circle with a radius of 1, which is widely used in mathematics, especially in trigonometry and coordinate geometry. Using GeoGebra commands such as Intersect, Point, Circle, Rotate, Mirror, etc., it dynamically shows points on the unit circle and their corresponding angles and coordinates. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

Intersect(xAxis, yAxis) → A
Point(yAxis) → B
Circle(A, B) → c
Intersect(c, xAxis, 2) → C
Rotate(C, 29.999999999999996°, A) → C'
Rotate(C, 45°, A) → C'_1
Rotate(C, 59.99999999999999°, A) → C'_2
Mirror(C', xAxis) → C''
Mirror(C'_1, xAxis) → D
Mirror(C'_2, xAxis) → E
Mirror(C'_2, yAxis) → F
Mirror(C'_1, yAxis) → G
Mirror(C', yAxis) → C''_1
Mirror(E, yAxis) → E'
Mirror(D, yAxis) → D'
Mirror(C'', yAxis) → C'''
Intersect(c, xAxis, 1) → H
Intersect(c, yAxis, 2) → I
Rotate(C, α, A) → C'_3
Angle(Z, A, C'_3) → β
Segment(A, C'_3) → f
Segment(C'_3, J) → g
Segment(A, J) → h
If(abs(sin(α)) ≟ 0.5 ∨ abs(cos(α)) ≟ 0.5 ∨ cos(α) ≟ 0 ∨ abs(sin(α)) ≟ 1 ∨ abs(sin(α)) ≟ sqrt(2) / 2, true, false) → d
Polygon(A, J, C'_3) → poly1, c'_3, a_1, j

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with a radius of 1. Start by finding the intersection of the x-axis and y-axis as point A, and take point B on the y-axis as the diameter to draw the unit circle c. Then, take point C on the x-axis and use rotation and reflection to generate points C', C'_1, C'_2, C'', C''_1, D, E, F, G. Finally, rotate and calculate the angle β to generate point C'_3 and draw the polygon connecting related points.

The prompt above was compiled from the original drawing commands and is for reference only.