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Evaluate Trig Functions Given a Point on the Terminal Ray

Evaluate Trig Functions Given a Point on the Terminal Ray
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2017-09-05 23:30
VectorFunctionTrigonometryGeometric Construction
In collections Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Trigonometric Functions of Angles
This example demonstrates how to evaluate the six trigonometric functions given a point on the terminal ray. Key mathematical concepts include trigonometric functions, vectors, and geometric constructions. Commands used include Segment, Ray, Point, Vector, Intersect, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(B, P) → g
  2. Random(-10, 10) → a
  3. Random(-10, 10) → b
  4. SurdText(r) → text1
  5. SurdText(sinangle) → text2
  6. SurdText(cosangle) → text3
  7. SurdText(tanangle) → text4
  8. SurdText(cosecantangle) → text5
  9. SurdText(secantangle) → text6
  10. SurdText(cotanangle) → text7
  11. Ray((0, 0), (1, 0)) → f
  12. Point(f) → A
  13. Angle(A, B, P) → α
  14. Vector(B, P) → u
  15. Intersect(h, i) → C
  16. Vector(B, C) → v
  17. Vector(C, P) → w
  18. Polygon(B, C, P) → poly1, p, b_1, c_2

AI Drawing Prompt Reference

Draw a figure with a point P on ray f starting from the origin along the positive x-axis. Construct vector u from point P and calculate the angle α between vector u and ray f. Use points B and P to construct vectors v and w, and triangle BPC. Draw directed segment g from point B to point P, and display the values of the six trigonometric functions: sin(α), cos(α), tan(α), csc(α), sec(α), and cot(α).
The prompt above was compiled from the original drawing commands and is for reference only.