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Unit Circle Exact Values by Kirsty Watts

Unit Circle Exact Values by Kirsty Watts
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2017-03-13 13:03
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between angles and trigonometric values on the unit circle. It involves core concepts like the unit circle, trigonometric functions, angles, and coordinate geometry. Construction highlights include using GeoGebra commands such as Point, Circle, Rotate, Angle, Intersect, and Segment to draw the unit circle, points, segments, and angles, and calculating intersections and rotations. Suitable for high school mathematics teaching to understand the definition and properties of trigonometric functions on the unit circle.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 1) → c
  3. Rotate(B, 45°, A) → B'
  4. Angle(B, A, B') → α
  5. Rotate(B, 30°, A) → B'_1
  6. Angle(B, A, B'_1) → β
  7. Point(c) → C
  8. Intersect(xAxis, yAxis) → D
  9. Segment(D, C) → f
  10. Angle(B, D, C) → δ

AI Drawing Prompt Reference

Draw a unit circle and mark points B' and B'_1 by rotating B 45 degrees and 30 degrees respectively around point A. Then pick a point D on the x-axis and draw a line segment from D to the point C on the circle. Finally, measure the angle BDC.
The prompt above was compiled from the original drawing commands and is for reference only.