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Unit Circle - Sin Cos Tan Cot Demo

Unit Circle - Sin Cos Tan Cot Demo
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2015-01-18 20:03
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric interpretation of sine, cosine, tangent, and cotangent functions using the unit circle. It involves core math concepts like the unit circle, trigonometric definitions, right triangles, and angle measurement. GeoGebra commands used include Intersect, Circle, Point, Segment, and OrthogonalLine for construction. Suitable for high school mathematics students and teachers to understand the relationship between trigonometric functions and the unit circle, or as a visual aid in introductory calculus teaching.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → B
  4. Segment(B, A) → Radius
  5. OrthogonalLine(B, yAxis) → d
  6. OrthogonalLine(B, xAxis) → b
  7. Intersect(b, xAxis) → D
  8. Segment(B, D) → sine
  9. Segment(A, D) → cosine
  10. OrthogonalLine(B, Radius) → a
  11. Intersect(a, xAxis) → C
  12. Intersect(a, yAxis) → E
  13. Segment(B, C) → tangent
  14. Segment(B, E) → cotangent
  15. Segment(D, C) → e

AI Drawing Prompt Reference

Draw a unit circle, mark the intersection points with the x-axis and y-axis, and draw a radius from the center to a point on the circle. From this point, draw perpendicular lines to the x-axis and y-axis, marking the intersection points. Connect the point on the circle to the x-axis intersection to form the sine line, and to the y-axis intersection to form the cosine line. Then, draw perpendicular lines from the point on the circle to the radius, marking the intersection points. Connect the point on the circle to the x-axis intersection to form the tangent line, and to the y-axis intersection to form the cotangent line. Finally, connect the x-axis intersection to the tangent line intersection.
The prompt above was compiled from the original drawing commands and is for reference only.