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Trigonometric Ratios by Kevin Agnew

Trigonometric Ratios by Kevin Agnew
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2019-03-09 02:19
AngleFunctionTrigonometry
This example demonstrates the ratio relationships of trigonometric functions in a triangle. Key mathematical concepts include sine, cosine, and tangent. Using commands like Intersect, Point, Circle, Segment, and OrthogonalLine, it constructs angles and segments. Suitable for middle school and above students to learn the basic properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → f
  6. OrthogonalLine(C, xAxis) → g
  7. Intersect(g, xAxis) → D
  8. Segment(A, D) → h
  9. Angle(C, A, D) → α
  10. Angle(C, D, A) → β
  11. Distance(f, g) → a
  12. Segment(C, D) → l
  13. Segment(C, D) → i
  14. Segment(A, C) → j
  15. Segment(C, D) → k
  16. Segment(A, C) → m
  17. Segment(A, D) → n
  18. Segment(C, D) → q
  19. Segment(A, D) → r

AI Drawing Prompt Reference

Draw a right triangle to demonstrate the ratio relationships of trigonometric functions. Start by plotting the x and y axes and finding their intersection at the origin. Draw a circle centered at the origin that intersects the x-axis at another point. Connect these two points to form one leg of the right triangle. From the circle's intersection point, draw a line perpendicular to the x-axis, which intersects the x-axis at another point. Connect the origin to this point to complete the right triangle. Label the three angles and draw the corresponding sides to illustrate the geometric meanings of sine, cosine, and tangent.
The prompt above was compiled from the original drawing commands and is for reference only.