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Trig Functions from the Unit Circle

Trig Functions from the Unit Circle
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2016-10-15 01:51
CircleFunctionTrigonometry
This example demonstrates how to represent trigonometric functions using points on the unit circle. Key mathematical concepts include trigonometric functions, the unit circle, and angles. Using GeoGebra commands such as Intersect, Point, Circle, and Rotate, the example dynamically illustrates the properties of sine and cosine functions. Suitable for high school math education and students learning trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → C
  2. Point(yAxis) → B
  3. Circle(C, B) → c
  4. Intersect(c, xAxis, 2) → A
  5. Rotate(A, θ, C) → P
  6. Angle(A, C, P) → α
  7. Ray(C, P) → a
  8. Midpoint(A, C) → D
  9. Midpoint(P, C) → E
  10. CircleArc(C, D, E) → d
  11. Sequence(Line[((i * 3.141592653589793 / 6), 0), yAxis], i, -12, 12) → list1
  12. Function(sin(x), 0, 6.283185307179586) → f
  13. Segment(G, F) → e
  14. Function(cos(x), 0, 6.28319) → g
  15. Segment(G, H) → h
  16. Function(tan(x), 0, 6.283185307179586) → p
  17. Segment(G, I) → j

AI Drawing Prompt Reference

Draw a unit circle and plot the sine and cosine values for angle θ. Start by drawing the intersection point C of the x-axis and y-axis, then draw circle c with C as the center and B as the radius. Find the two intersection points A and A' of circle c with the x-axis, and rotate point A around C to get point P. Draw ray a with the angle α between line AC and the x-axis. Then, draw the midpoints D and E of segments AC and PC, and draw arc d with D and E as endpoints. Next, draw 12 rays starting from C, each separated by π/6 radians, forming a grid. Finally, draw the sine function f, cosine function g, and tangent function p from the origin to 6.283185307179586π.
The prompt above was compiled from the original drawing commands and is for reference only.