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CAST and Tan Graph

CAST and Tan Graph
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2018-12-14 19:30
FunctionTrigonometryGeometric Construction
This example demonstrates the characteristics of the tangent function in different quadrants. It involves core trigonometric concepts and uses GeoGebra commands such as Point, Vector, Circle, etc., to show the changes of the tangent function in each quadrant. Suitable for high school math education and learning, helping students understand the periodicity and odd-even properties of the tangent function.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (-1, 0)]) → B
  2. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  3. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  4. Circle(B, A) → c
  5. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  6. Vector((0 - x(Q), 0), (x(Corner[2]), 0)) → z
  7. Sequence(Segment[((0.75 * i), 0), ((0.75 * i), -0.025)], i, -4, 4) → list1
  8. Sequence(Segment[(x(B), (0.5 * i) - 1), (x(B) - 0.025, (0.5 * i) - 1)], i, 0, 4) → list3
  9. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  10. Segment(A, ((-x(Q)), 0)) → d
  11. Textfield(atantheta) → InputBox1
  12. Segment(P, (x(P), 0)) → r
  13. Segment(D, A) → j
  14. Angle(A, B, D) → β
  15. Sequence(Segment[(0, (0.5 * i) - 1), (-0.025, (0.5 * i) - 1)], i, -2, 6) → list2
  16. Segment(B, D) → i
  17. Segment(B, A) → k
  18. Intersect(c, i) → C,
  19. Rotate(C, π, B) → C'
  20. Segment(C', B) → l
  21. Angle(A, B, C') → γ