MathPlotAI Logo MathPlotAI

Even/Odd Trig Identities Demo

Even/Odd Trig Identities Demo
Loading the math board and drawing, please wait…
2018-12-05 01:57
FunctionTrigonometryGeometric Construction
This example demonstrates the odd and even properties of trigonometric functions through dynamic geometry. It involves core concepts like sine, cosine, piecewise functions, limits, planes, parabolas, and equations. Construction highlights include using GeoGebra commands such as Point, Angle, Segment, If, and Intersect. Suitable for high school mathematics education to understand trigonometric identities and function graphing.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Angle(C, (0, 0), A) → α
  3. Segment((0, 0), C) → f
  4. Segment((0, 0), A) → g
  5. If(a < 1, Rotate[g, ((-2 * α) * a), (0, 0)], Rotate[g, (-2 * α), (0, 0)]) → i
  6. If(1 < a < 2, Segment[A, (x(A), y(A) - ((a - 1) * (2 * y(A))))], a ≥ 2, Segment[A, (x(A), (-y(A)))]) → h
  7. Intersect(i, h) → B
  8. Angle(B, (0, 0), C) → β
  9. If(2 < a < 2.5, Segment[(0, 0), (((2 * (a - 2)) * x(A)), 0)], a ≥ 2.5, Segment[(0, 0), (x(A), 0)]) → j

AI Drawing Prompt Reference

Draw a demonstration of trigonometric function odd and even properties, including the origin O, point A and C, and a segment g rotating around O by -2α or (-2α)*a degrees based on parameter a. Segment h extends from A downwards or to the negative y-axis based on a, intersecting with segment i at point B. Finally, draw a line from O to the x-axis or point (x,A) based on a.
The prompt above was compiled from the original drawing commands and is for reference only.