MathPlotAI Logo MathPlotAI

Unit Circle with Trigonometric Measurements

Unit Circle with Trigonometric Measurements
Loading the math board and drawing, please wait…
2018-05-05 12:51
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric representation of trigonometric values on the unit circle, visually showcasing concepts like sine, cosine, tangent, and angle measurement. Core math concepts include the unit circle, trigonometric functions, angle measurement, and right triangles. Construction highlights GeoGebra commands such as Intersect, Point, Circle, Segment, OrthogonalLine, Tangent, and Distance. Ideal for high school students learning trigonometric definitions and geometry, or university foundational mathematics education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → C
  3. Circle(A, C) → c
  4. Point(c) → D
  5. Segment(A, D) → f
  6. OrthogonalLine(D, xAxis) → g
  7. Intersect(g, xAxis) → E
  8. Segment(D, E) → sine
  9. OrthogonalLine(D, yAxis) → i
  10. Intersect(i, yAxis) → F
  11. Segment(D, F) → cosine
  12. Tangent(D, c) → k,
  13. Intersect(k, xAxis) → G
  14. Intersect(k, yAxis) → H
  15. Segment(H, G) → l
  16. Segment(A, G) → secant
  17. Segment(A, H) → cosecant
  18. Segment(H, D) → cotangent
  19. Segment(D, G) → tangent
  20. Intersect(c, c) → J, , ,
  21. Distance(tangent, cotangent) → a

AI Drawing Prompt Reference

Draw a unit circle and mark a point D on it, representing an angle θ. From point D, draw a perpendicular to the x-axis and another to the y-axis, intersecting the axes at points E and F respectively. Then, draw a tangent from D to the circle, intersecting the x-axis and y-axis at points G and H. Connect points A and D, D and E, D and F, D and G, D and H, A and G, and A and H to form the sine, cosine, tangent, cotangent, secant, and cosecant line segments, illustrating the trigonometric values on the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.