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Activity #4_The Basics of Sine and Cosine

Activity #4_The Basics of Sine and Cosine
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2019-09-04 08:42
AngleTrigonometryGeometric Construction
In collections Sections 9.4 and 9.5__3 Trig Ratios
This example demonstrates the constancy of side ratios in similar right triangles through interactive exploration, reinforcing the AA similarity theorem and trigonometric definitions. Students observe that ratios of sides (sin, cos) remain constant across similar triangles. Constructed using GeoGebra commands like Ray, OrthogonalLine, Point, Rotate, etc., it is ideal for high school trigonometry instruction. Focuses on similarity, trigonometric functions, and geometric constructions.

GeoGebra Commands & Parameters

  1. Ray(A, C) → a_1
  2. OrthogonalLine(C, a_1) → b
  3. Point(b) → C_1
  4. Ray(C, C_1) → c
  5. Rotate(C, β, A) → B'
  6. Angle(C, A, B') → α
  7. Ray(A, B') → d
  8. Intersect(c, d) → D
  9. Segment(A, D) → hyp
  10. Segment(A, C) → adj
  11. Segment(C, D) → opp
  12. Angle(D, C, A) → γ
  13. Polygon(A, C, D) → poly1, d_1, a, b_1