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Unit Circle and Trigonometry by Matthew Kiss

Unit Circle and Trigonometry by Matthew Kiss
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2013-08-12 12:05
CircleAngleFunctionTrigonometryGeometric Construction
This example demonstrates the calculation of trigonometric ratios using a unit circle. It involves core math concepts like the unit circle, trigonometric functions (sine, cosine, tangent), angles, and the relationship between the sides of a right triangle. GeoGebra commands and objects such as Point, Intersect, Circle, Angle, Segment, OrthogonalLine, Polygon, and Distance are used to construct the unit circle, angles, triangles, and text annotations. It is suitable for high school students learning and understanding the geometric definition of trigonometric functions.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Intersect(xAxis, yAxis) → A
  3. Circle(A, B) → c
  4. Point(c, f) → C
  5. Angle(B, A, C) → α
  6. Segment(C, A) → a
  7. Segment(C, B) → b
  8. Segment(B, A) → d
  9. OrthogonalLine(C, d) → e
  10. OrthogonalLine(C, yAxis) → g
  11. Polygon(C, A, B) → poly1, b_1, c_1, a_1
  12. Distance(C, B) → distanceCB

AI Drawing Prompt Reference

Draw a unit circle with the intersection point of the x-axis and the center as one point, and another point on the x-axis. Connect these two points to form the circle. Mark a point on the circle, connect it to the center and the intersection point with the x-axis to form a right triangle. Label the lengths of the triangle's sides and draw a perpendicular line from the point on the circle to the x-axis. Show the three angles of the triangle and label the three vertices of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.