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Tan(x) & Unit Circle - Radians

Tan(x) & Unit Circle - Radians
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2014-01-07 02:32
CircleAngleTrigonometry
In collections Trigonometry: Basic and More
This example demonstrates the relationship between the tangent function and the unit circle, helping students understand the connection between radian measure and trigonometric values. Through steps like constructing arcs, rotating, and measuring angles, students can visually see how angles in radians correspond to their tangent values. Suitable for middle school and above students learning trigonometry.

GeoGebra Commands & Parameters

  1. Line(B, O) → a
  2. Circle(O, 1) → c
  3. Intersect(c, a, 2) → C
  4. Rotate(C, α, O) → D
  5. CircleArc(O, J, D) → k
  6. Angle(C, O, D) → β
  7. Segment(O, D) → b
  8. Distance(D, a) → d
  9. OrthogonalLine(D, a) → e
  10. Intersect(a, e) → A
  11. Length(k) → RadianAlpha
  12. Segment(D, A) → g
  13. Segment(A_1, D_1) → h
  14. Midpoint(D, A) → E1
  15. Midpoint(A_1, D_1) → F
  16. Point(xAxis) → G
  17. Segment(G, A_1) → i
  18. Intersect(c, a, 2) → H
  19. Intersect(c, a, 1) → I
  20. Segment(I, H) → j
  21. Segment(O, A) → l
  22. Midpoint(O, A) → E2
  23. Polygon(E, K, L, M) → poly1, e_1, k_1, l_1, m

AI Drawing Prompt Reference

Draw a unit circle and mark a point on it. Draw a line segment from the center to this point. Construct an angle with the line segment as one side, where the other side intersects the circle at another point. Rotate this angle to align with the initial line segment and draw the arc of rotation. Measure the angle of rotation and display its radian value on the graph. Draw a perpendicular line from the rotated point to the initial line segment, and mark the intersection point. Connect the rotated point to the foot of the perpendicular. Finally, combine the unit circle, line segment, angle, and rotation arc into a single graphic to illustrate the relationship between the tangent function and the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.