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Demonstration of Sine and Cosine

Demonstration of Sine and Cosine
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2015-12-07 08:07
CircleAngleFunctionTrigonometryGeometric Construction
This example dynamically demonstrates the geometric meaning of sine and cosine values in a right triangle. It involves core math concepts like trigonometric function definitions, unit circle, and the relationship between angles and side lengths. Construction highlights the use of commands/objects such as Circle, Intersect, Point, Segment, Angle, and LaTeX. Suitable for high school mathematics teaching to understand the connection between trigonometric functions and geometric figures.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → c_1
  2. Intersect(xAxis, yAxis) → A
  3. Point(c_1) → B
  4. Segment(A, B) → a
  5. Intersect(c_1, xAxis, 2) → C
  6. Segment(A, C) → b
  7. Angle(b, a) → θ
  8. Segment(D, C) → d
  9. Segment(B, E) → c
  10. LaTeX(Sine, true, true) → text1
  11. LaTeX(θ, true, true) → text2
  12. Segment(B, G) → g
  13. LaTeX(Cosine, true, true) → text3