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Quadrant Rule for Trigonometric Ratios

Quadrant Rule for Trigonometric Ratios
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2016-05-31 21:22
AngleTrigonometryGeometric Construction
This example demonstrates the sign variation of trigonometric ratios (sine, cosine, tangent) in different quadrants. Key math concepts include quadrants, trigonometric functions, and their sign rules. GeoGebra commands and objects used are Intersect, Circle, Rotate, Angle, Segment, OrthogonalLine, with objects like O, B, θ, A. Suitable for high school students to learn and understand the basic properties of trigonometric functions, ideal for classroom demonstrations or homework practice.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, B) → c_1
  3. Rotate(B, θ, O) → A
  4. Angle(B, O, A) → α
  5. Segment(A, O) → r
  6. Segment(A, (x(A), 0)) → b
  7. Intersect(b, xAxis) → M
  8. Segment(O, M) → a
  9. Angle(A, O, B) → β
  10. Intersect(c_1, yAxis, 2) → F
  11. Intersect(c_1, yAxis, 1) → C
  12. Segment(F, C) → c
  13. Intersect(c_1, xAxis, 2) → D
  14. Intersect(c_1, xAxis, 1) → E
  15. Segment(D, E) → d
  16. OrthogonalLine(G, xAxis) → f

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with horizontal x-axis and vertical y-axis. Place point B on the positive x-axis and point A on the circle such that rotating from B to A counterclockwise by angle θ. Connect O to A as a radius, drop a perpendicular from A to the x-axis meeting at M, and connect O to M. Label angles B-O-A and A-O-B. Draw a vertical diameter through the circle's intersections with the y-axis and a horizontal diameter through its intersections with the x-axis. Finally, from another point G on the circle, drop a perpendicular to the x-axis. This illustrates the sign changes of trigonometric ratios across quadrants.
The prompt above was compiled from the original drawing commands and is for reference only.