MathPlotAI Logo MathPlotAI

Tangent Graph from Unit Circle

Tangent Graph from Unit Circle
Loading the math board and drawing, please wait…
2018-02-08 05:09
CircleFunctionTrigonometryGeometric ConstructionGraphing
This example demonstrates how to construct the tangent function graph by rotating points on a unit circle. Core math concepts include the unit circle, trigonometric functions, the definition of the tangent function, and angle rotation. GeoGebra commands and objects used in the construction are Point, Rotate, Segment, Angle, Circle, Vector, Sequence, and Function. Suitable for high school students learning about the geometric origin and graph characteristics of the tangent function.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (-1, 0)]) → B
  2. Rotate(A, θ, B) → P
  3. Segment(A, Intersect[Line[B, P], x = x(A)]) → h
  4. Segment(P, Intersect[Line[B, P], x = x(A)]) → g
  5. Rotate(A, θ, B) → A'
  6. Angle(A, B, A') → α
  7. Rotate(A, θ, B) → A'_1
  8. Angle(A, B, A'_1) → β
  9. Segment(Q, (x(Q), 0)) → e
  10. Circle(B, A) → c
  11. Segment(B, P) → a
  12. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  13. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  14. Vector((0, 0), (x(Corner[2]), 0)) → z
  15. Sequence(Segment[((0.75 * i), 0), ((0.75 * i), -0.025)], i, 1, 4) → list1
  16. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  17. Sequence(Segment[(0, (0.5 * i) - 1), (-0.025, (0.5 * i) - 1)], i, 0, 4) → list2
  18. Sequence(Segment[(x(B), (0.5 * i) - 1), (x(B) - 0.025, (0.5 * i) - 1)], i, 0, 4) → list3
  19. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  20. Segment(C, Q) → d
  21. Function(tan((120° * x)), 0, (θ / ((360 * γ)) * 3)) → f
  22. Point(Ray[(0, 0), (-1, 0)]) → B_1
  23. Rotate(A_1, θ, B_1) → P_1
  24. Rotate(A_1, θ, B_1) → A'_2
  25. Rotate(A_1, θ, B_1) → A'_3
  26. Circle(B_1, A_1) → c_1

AI Drawing Prompt Reference

Draw a unit circle and mark points to construct the graph of the tangent function. Start by drawing a ray from the origin to the left, intersecting the x-axis at point B. Rotate point A around B by angle θ to get point P. Draw perpendiculars from P and A to the x-axis, meeting at points g and h respectively. Rotate A around B again to get A', and draw the angle α between A and B. Further rotate A' around B to get A'_1, and draw the angle β between A and A'_1. Mark point Q on the x-axis and draw the perpendicular line e from Q to the x-axis. Draw a circle c with center B and radius A, and draw the line segment a from B to P. Finally, draw the graph of the tangent function and add auxiliary line segments and markings to illustrate the geometric construction of the tangent function.
The prompt above was compiled from the original drawing commands and is for reference only.