MathPlotAI Logo MathPlotAI

The Derivative of Sine at x=0

The Derivative of Sine at x=0
Loading the math board and drawing, please wait…
2018-01-25 11:45
FunctionTrigonometryCalculusDerivativeGeometric Construction
This example demonstrates the calculation and geometric interpretation of the derivative of the sine function at x=0. It involves core mathematical concepts such as the definition of derivatives, limits, and properties of trigonometric functions. The construction uses GeoGebra commands and objects like Point, Vector, Textfield, Segment, Line, Derivative, Intersect, Polygon, and Sequence. It is suitable for high school and above students learning calculus and the geometric meaning of function derivatives, or for teaching purposes.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Vector(A, B) → f
  3. Textfield(f_1) → inputBox1
  4. Vector(x_1, y_1) → v
  5. Segment(f_a, F) → c
  6. Segment(E, F) → d
  7. Segment(A, x_1) → e
  8. Segment(B, y_1) → h
  9. Line(x_1, y_1) → i
  10. Textfield(f_1) → inputBox2
  11. Derivative(f_1) → q
  12. Segment(C, D) → b
  13. Segment((0, y(A) - δ), (0, y(A) + δ)) → m
  14. Point(m) → G
  15. Point(m) → H
  16. Point(yAxis) → I
  17. Vector(I, J) → u
  18. Intersect(n, p) → K
  19. Intersect(a, p) → L
  20. Intersect(a, r) → M
  21. Intersect(n, r) → N
  22. Polygon(K, L, M, N) → poly1, k_1, l_1, m_1, n_1
  23. Sequence((0, xk), xk, y(A) - δ, y(A) + δ, δ / 8) → testx
  24. Sequence((2, f_1(xk)), xk, y(A) - δ, y(A) + δ, δ / 8) → testy
  25. Sequence(Vector[(0, xk), (2, f_1(xk))], xk, y(A) - δ, y(A) + δ, δ / 8) → list1
  26. Textfield(ε) → inputBox3
  27. Textfield(δ) → inputBox4
  28. Vector(I, Pcos) → w