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Tangent of Any Angle

Tangent of Any Angle
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2023-03-14 04:00
FunctionTrigonometryCoordinate GeometryParametric EquationGeometric Construction
In collections geometriadinamica.es
This example demonstrates the geometric meaning of the tangent function for any angle, dynamically constructing right triangles to show the relationship between the tangent value and the angle. Core mathematical concepts include trigonometric functions, right triangles, angle measurement, and geometric construction. It leverages GeoGebra commands such as Intersect, Circle, Rotate, Angle, Segment, OrthogonalLine, Line, and Polygon. Suitable for high school students learning trigonometric definitions and properties, or for understanding the geometric interpretation of derivatives in calculus.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle((0, 0), 1) → c
  3. Intersect(c, xAxis, 2) → A
  4. Rotate(A, (ángulo * pi / 180), O) → P
  5. Angle(A, O, P) → α
  6. Segment(P, O) → b
  7. Segment(D, O) → cos
  8. OrthogonalLine(A, xAxis) → a
  9. Line(O, P) → d
  10. Intersect(d, a) → B
  11. Segment(B, A) → e
  12. Polygon(B, O, A) → Q, a_1, b_1, o
  13. Segment(C, B) → f
  14. Segment(P, D) → sen

AI Drawing Prompt Reference

Draw a coordinate plane with the origin and both coordinate axes. Construct a circle centered at the origin with radius 1, then choose the intersection point A of the circle with the horizontal axis. Rotate A about the origin by a variable angle to get point P, forming an angle α at the origin. Draw the segment from the origin to P, construct the perpendicular from P to the horizontal axis, and intersect it with the line through the origin and P to obtain point B. Connect B to A and form a polygon using B, the origin, and A. Let the figure update as the angle changes and include the indicated segment parts related to cosine and sine.
The prompt above was compiled from the original drawing commands and is for reference only.