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Sine on the Unit Circle

Sine on the Unit Circle
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2018-01-25 02:45
CircleTrigonometryGeometric Construction
This example demonstrates the geometric meaning of the sine function on the unit circle. Key mathematical concepts include the sine function, unit circle, and angles. By constructing a circle, sine lines, and angles, the periodicity and symmetry of the sine function are illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c) → C
  5. OrthogonalLine(C, xAxis) → f
  6. Segment(A, C) → Radius
  7. Intersect(f, xAxis) → D
  8. Segment(C, D) → sine
  9. Intersect(c, xAxis, 2) → E
  10. Intersect(c, xAxis, 1) → F
  11. Segment(E, F) → g
  12. Angle(g, Radius) → α
  13. CircleArc(A, F, C) → d
  14. Segment(A, D) → cosine

AI Drawing Prompt Reference

Draw a unit circle with its center at the origin and radius of 1. From a point C on the circle, draw a perpendicular line f to the x-axis. Connect the center A and point C to form the radius. From point C, draw a perpendicular line f to the x-axis and find its intersection D with the x-axis. Connect C and D to form the sine segment. Find the second and first intersections E and F of the circle with the x-axis, and connect E and F to form segment g. Measure the angle α formed by segment g and the radius. Draw an arc d from A to F. Finally, connect A and D to form the cosine segment.
The prompt above was compiled from the original drawing commands and is for reference only.