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Sine and Cosine Defined with a Triangle

Sine and Cosine Defined with a Triangle
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2014-02-18 02:12
TriangleAngleFunctionTrigonometryGeometric Construction
Drag point A to draw the graphs of sine and cosine. This example demonstrates the definitions of sine and cosine in a right triangle. GeoGebra commands such as Point, Segment, Midpoint, Circle, and Angle are used to construct the diagram. Suitable for high school mathematics education and learning trigonometric functions.

GeoGebra Commands & Parameters

  1. Point(Circle[A_1, 1]) → B
  2. Segment(A_1, B) → hyp
  3. Midpoint(hyp) → C
  4. Circle(C, B) → c
  5. Point(c) → A
  6. Segment(A_1, A) → adj
  7. Segment(A, B) → opp
  8. Angle(B, A, A_1) → α_1
  9. Angle(A, A_1, B) → α

AI Drawing Prompt Reference

Draw a right triangle with point A moving on the unit circle, point A_1 at the origin, and point B on the unit circle. Connect point A_1 and point B to form the hypotenuse, with point C as the midpoint. Draw a circle centered at point C with point B on the circumference. Point A moves on the circle, connecting point A_1 and point A to form the adjacent side, and connecting point A and point B to form the opposite side. Construct angle α_1 with point B, point A, and point A_1, and construct angle α with point A, point A_1, and point B.
The prompt above was compiled from the original drawing commands and is for reference only.