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Derivative of Sine and Cosine Functions

Derivative of Sine and Cosine Functions
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2018-01-26 09:41
FunctionTrigonometryCalculusDerivativeGeometric Construction
This example demonstrates the derivatives of sine and cosine functions. Key mathematical concepts include derivatives and trigonometric functions. Using GeoGebra commands, it shows how to analyze the rate of change of sine and cosine functions through vectors, functions, and derivatives. Suitable for high school calculus education.

GeoGebra Commands & Parameters

  1. Element(fnlist, fn) → f_1
  2. Point(yAxis) → A
  3. Vector(A, B) → f
  4. Textfield(f_1) → inputBox1
  5. Vector(x_1, y_1) → v
  6. Segment(f_x, F) → c
  7. Segment(E, F) → d
  8. Segment(A, x_1) → e
  9. Segment(B, y_1) → g
  10. Segment(B, y_1) → Δseg
  11. Line(x_1, y_1) → i
  12. Line(A, B) → k
  13. Intersect(i, k) → Focus
  14. Textfield(f_1) → inputBox2
  15. Line(f_x, E) → secant
  16. Derivative(f_1) → h
  17. Line(f_x, Vector[(0, 0), (1, h(y(A)))]) → tangent
  18. Vector(B, C) → u
  19. Vector(B, Est') → w

AI Drawing Prompt Reference

Draw the derivative graphs of sine and cosine functions. First, plot the sine and cosine functions, then analyze their derivatives using vectors and functions to show the secant and tangent lines, and finally draw the tangent line based on the point of tangency and the derivative value.
The prompt above was compiled from the original drawing commands and is for reference only.