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Six Trigonometric Functions Quick Illustrator

Six Trigonometric Functions Quick Illustrator
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2021-09-15 18:28
CircleFunctionTrigonometryGeometric Construction
In collections Trigonometric Functions of Angles
This example demonstrates the definitions and relationships of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) on the unit circle. It involves core mathematical concepts such as trigonometric functions, unit circle, angles, vectors, and geometric constructions. The construction uses GeoGebra commands like Point, Intersect, Circle, Ray, Angle, OrthogonalLine, Vector, and Segment. It is suitable for high school students learning the basic properties and interrelations of trigonometric functions.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (1, 0)]) → A
  2. Intersect(xAxis, yAxis) → B
  3. Circle(B, A) → c
  4. Point(c) → C
  5. Ray(B, C) → f
  6. Angle(A, B, C) → α
  7. OrthogonalLine(C, xAxis) → g
  8. Intersect(g, xAxis) → D
  9. Vector(B, D) → u
  10. Vector(D, C) → v
  11. Segment(B, C) → h

AI Drawing Prompt Reference

Draw the unit circle with six trigonometric functions: Start by drawing a horizontal ray from the origin, determine the center B and point A, and draw the unit circle c with B as the center and A as the radius. Take a point C on circle c, draw a ray f from B, forming angle α with the x-axis. Construct a perpendicular line g from C to the x-axis, intersecting at point D. Connect BD and DC to get vectors u and v. Finally, connect B and C to form segment h.
The prompt above was compiled from the original drawing commands and is for reference only.