MathPlotAI Logo MathPlotAI

Trigonometric Ratios of General Angle Activity Sheet

Trigonometric Ratios of General Angle Activity Sheet
Loading the math board and drawing, please wait…
2018-09-07 07:03
TriangleCircleAngleGeometric Construction
This activity sheet demonstrates the trigonometric ratios of general angles using dynamic geometry software. Key mathematical concepts include trigonometric function definitions, the relationship between angles and ratios, and geometric construction of proportions. Construction involves using GeoGebra commands like Circle, Point, Segment, Midpoint, Angle, and Textfield to build triangles and circles, with parameter input via InputBox. Suitable for middle school students or high school students to understand trigonometric applications in geometry and master angle-to-ratio conversion techniques.

GeoGebra Commands & Parameters

  1. Circle(O, D) → c
  2. Point(c) → P
  3. Segment(O, P) → f
  4. Midpoint(O, P) → C
  5. Segment(P_x, P) → g
  6. Segment(O, P_x) → h
  7. Midpoint(h) → A
  8. Midpoint(g) → B
  9. Angle(P_x, O, P) → α
  10. Textfield(D) → InputBox1
  11. Angle(xAxis, f) → β
  12. If(β < 90°, 1, If[β < 180°, 2, If[β < 270°, 3, 4]]) → quadnum
  13. Textfield(θ_{inputd}) → InputBox2
  14. Textfield(θ_{inputr}) → InputBox3
  15. Textfield(numrev) → InputBox4
  16. If(quadnum > 1 ∧ quadnum < 4, If[Defined[α], -1, 1], 1) → signadjxquad
  17. If(quadnum > 2, If[Defined[α], -1, 1], 1) → signoppyquad
  18. Point(c) → P''
  19. Segment(O, P'') → i
  20. Segment(P''_x, P'') → j
  21. Segment(O, P''_x) → k
  22. Angle(P''_x, O, P'') → γ
  23. Angle(xAxis, i) → δ
  24. If(δ < 90°, 1, If[δ < 180°, 2, If[δ < 270°, 3, 4]]) → quadnumP''
  25. If(quadnumP'' > 1 ∧ quadnumP'' < 4, If[Defined[γ], -1, 1], 1) → signadjxquadP''
  26. If(quadnumP'' > 2, If[Defined[δ], -1, 1], 1) → signoppyquadP''
  27. Midpoint(j) → F
  28. Midpoint(k) → G
  29. Midpoint(i) → H
  30. Textfield(textmAngleLable1) → InputBox5
  31. Textfield(textmAngleLabel2) → InputBox6
  32. Textfield(textmadjx) → InputBox7
  33. Textfield(textmoppy) → InputBox8
  34. Textfield(texthypo) → InputBox9
  35. Textfield(textmadjxP'') → InputBox10
  36. Textfield(textmoppyP'') → InputBox11
  37. Textfield(texthypoP'') → InputBox12
  38. Angle(f, xAxis) → ε