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Trigonometric Ratios on the Cartesian Plane

Trigonometric Ratios on the Cartesian Plane
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2016-08-01 02:06
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to visualize trigonometric ratios (sine, cosine, tangent) on the Cartesian plane by constructing right-angled triangles. Key math concepts include trigonometry, coordinate geometry, and properties of right triangles. It uses GeoGebra commands like Intersect, Rotate, Angle, OrthogonalLine, Polygon, and LaTeX for construction. Suitable for high school students learning the representation and application of trigonometric functions in a coordinate system.

GeoGebra Commands & Parameters

  1. Intersect(c, xAxis, 2) → A
  2. Intersect(xAxis, yAxis) → B
  3. Rotate(A, θ°, B) → P
  4. Angle(A, B, P) → α
  5. OrthogonalLine(P, xAxis) → a
  6. Intersect(a, xAxis) → C
  7. Polygon(P, C, B) → poly1, b, p, c_1
  8. LaTeX(tan, true, true) → text1
  9. LaTeX(sin, true, true) → text2
  10. LaTeX(cos, true, true) → text3
  11. LaTeX(cosec, true, true) → text4
  12. LaTeX(sec, true, true) → text5
  13. LaTeX(cot, true, true) → text6