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Trigonometric Ratios in the Unit Circle

Trigonometric Ratios in the Unit Circle
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2014-10-21 08:26
CircleTrigonometryGeometric Construction
This example demonstrates the trigonometric ratios in the unit circle. Through the unit circle, users can intuitively understand the concepts of basic trigonometric functions such as sine, cosine, and tangent. The construction uses GeoGebra commands like Circle, Intersect, and Point to dynamically explore the properties of trigonometric functions. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → C
  2. Point(xAxis) → S
  3. Circle(C, S) → c
  4. Point(c) → P
  5. OrthogonalLine(P, xAxis) → a
  6. Intersect(a, xAxis) → Q
  7. Polygon(C, Q, P) → poly1, b, a_1, c_1
  8. Angle(P, C, S) → α
  9. Segment(C, P) → g

AI Drawing Prompt Reference

Draw a unit circle, mark the intersection point of the circle's center with the x-axis, draw a line from this point to the circle, and label the intersection point on the circle. Connect this point to the center, then draw a perpendicular line from this point to the x-axis. Highlight the triangle formed by the center, the foot of the perpendicular, and the intersection point on the circle, and label the angle at the center to illustrate trigonometric ratios in the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.