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Cosine Ratios in a Unit Circle

Cosine Ratios in a Unit Circle
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2017-05-18 15:43
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how cosine ratios are defined through right triangles in a unit circle. Key math concepts include the unit circle, cosine function, and right triangle side length relationships. GeoGebra commands used in construction are Intersect, Circle, Point, Segment, Line, OrthogonalLine, Midpoint, Angle, and Polygon. Suitable for high school students learning trigonometric definitions and properties.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Point(c) → C
  4. Segment(C, A) → a
  5. Line(C, yAxis) → b
  6. OrthogonalLine(A, yAxis) → d
  7. Intersect(b, d) → D
  8. Segment(C, D) → e
  9. Midpoint(D, C) → E
  10. Intersect(c, d, 1) → F
  11. Angle(F, A, C) → α
  12. Midpoint(C, A) → G
  13. Polygon(H, I, 4) → poly1, h, i, f, g, J, K
  14. Polygon(H_1, I_1, 4) → poly1_1, h_1, i_1, f_1, g_1, J_1, K_1
  15. Polygon(H_2, I_2, 4) → poly1_2, h_2, i_2, f_2, g_2, J_2, K_2
  16. Polygon(H_3, I_3, 4) → poly1_3, h_3, i_3, f_3, g_3, J_3, K_3
  17. Segment(A, D) → j