MathPlotAI Logo MathPlotAI

Trigonometry Ratios Demo

Trigonometry Ratios Demo
Loading the math board and drawing, please wait…
2019-04-19 03:38
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric relationship between trigonometric functions, circles, and points. It involves core concepts like the definition of trigonometric functions, properties of circles, and coordinate geometry. Construction highlights include using GeoGebra commands such as Intersect, Circle, Sequence, Point, Segment, Midpoint, and Angle. Suitable for high school mathematics education to understand the geometric meaning and construction methods of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c_1
  3. Intersect(c_1, xAxis, 2) → A
  4. Sequence(Rotate[A, k°, (0, 0)], k, 0, 360) → list1
  5. Point(list1) → P
  6. Segment(O, P) → c
  7. Segment(O, H) → b
  8. Segment(P, H) → a
  9. Midpoint(P, O) → M_r
  10. Midpoint(b) → M_x
  11. Midpoint(a) → M_y
  12. Angle(A, O, P) → θ

AI Drawing Prompt Reference

Draw a unit circle centered at the origin. Mark the intersection of the circle with the positive x-axis as a starting point. Place a movable point on the circle. Connect the center to this point with a segment. From the point, drop a perpendicular to the x-axis, marking the foot on the axis. Connect the center to this foot. This forms a right triangle with one leg on the x-axis. Mark the midpoints of the hypotenuse, the horizontal leg, and the vertical leg. Finally, indicate the angle at the center between the starting point and the movable point, showing its measure.
The prompt above was compiled from the original drawing commands and is for reference only.