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Trig Functions and the Unit Circle by Dr Adrian Jannetta

Trig Functions and the Unit Circle by Dr Adrian Jannetta
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2013-07-04 18:21
CircleFunctionTrigonometry
This example demonstrates the relationship between the angle θ on a unit circle and the trigonometric functions sine and cosine. Using commands like Intersect, Circle, Segment, Function, Angle, and Textfield, it visually explains the definition and geometric meaning of trigonometric functions. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c
  3. Segment(O, P) → a
  4. Function(sin(x), 0, θ) → p
  5. Angle(xAxis, a) → β
  6. Segment(O, Q_x) → b
  7. Segment(Q_x, P) → d
  8. Function(cos(x), 0, θ) → q
  9. Function(tan(x), 0, θ) → r
  10. Textfield(θ) → inputBox1

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with a radius of 1. Draw a ray from the origin to point P, representing angle θ. Draw a line segment a from the origin to point P, representing the sine of θ. Draw a perpendicular line segment b from the origin to the projection of P on the x-axis, representing the cosine of θ. Draw a line segment d from the projection of P on the x-axis to point P, representing the tangent of θ. Below the graph, include an input box for the value of angle θ.
The prompt above was compiled from the original drawing commands and is for reference only.