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Tangent and Cotangent

Tangent and Cotangent
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2019-02-20 23:09
FunctionTrigonometryGeometric Construction
In collections MalinC's GeoGebra-book
This example illustrates the concepts of tangent and cotangent. It involves basic trigonometric concepts such as the definitions and representations of tangent and cotangent on the unit circle. Using GeoGebra commands like Point, Circle, Angle, Intersect, etc., these geometric figures can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → O
  2. Point(xAxis) → B
  3. Circle(O, B) → c
  4. Point(c) → A
  5. Angle(B, O, A) → α
  6. OrthogonalLine(A, xAxis) → f
  7. Intersect(f, xAxis) → C
  8. Polygon(O, C, A) → t1, a, o, c_1
  9. OrthogonalLine(A, yAxis) → i
  10. Intersect(i, yAxis) → D
  11. OrthogonalLine(B, xAxis) → m
  12. Line(O, A) → n
  13. Intersect(n, m) → P
  14. Polygon(C, B, P, A) → q1, c_2, b, p, a_1
  15. Intersect(n, g) → Q
  16. Intersect(g, yAxis) → F
  17. Polygon(O, Q, F) → t2, f_1, o_1, e

AI Drawing Prompt Reference

Draw a coordinate plane with a unit circle centered at the origin. Mark the intersections of the circle with the x-axis and y-axis. Choose a point on the circle and draw a radius from the origin to this point, labeling the angle between the radius and the positive x-axis. From this point, drop perpendiculars to both axes, marking the feet. Through the x-axis intersection, draw a vertical line that meets the extended radius, forming a right triangle. Similarly, through a point on the y-axis, draw a horizontal line that meets the extended radius and the y-axis, forming another triangle. This illustrates the geometric definitions of tangent and cotangent on the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.