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Limits of Sine and Cosine

Limits of Sine and Cosine
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2016-09-25 11:32
FunctionTrigonometryCalculusLimitGeometric Construction
This example demonstrates the behavior of sine and cosine functions near specific points, focusing on their limits. Key math concepts include limits, trigonometric functions, and geometric constructions. It uses commands like Semicircle, Point, Segment, Intersect, CircleArc, and Angle in GeoGebra. Suitable for high school and above students to understand the limit properties of trigonometric functions in calculus.

GeoGebra Commands & Parameters

  1. Semicircle((0, 1), (0, -1)) → c
  2. Point(c) → A_1
  3. Segment((0, 0), A_1) → f
  4. Intersect(f, xAxis) → B_1
  5. Intersect(c, xAxis, 1) → A
  6. CircleArc(B_1, A, A_1) → d
  7. Angle(A, B_1, A_1) → α
  8. Segment(A_1, B) → g
  9. Segment(A_1, A) → h
  10. Angle(A_1, B_1, A) → β
  11. CircleArc(B_1, A_1, A) → e
  12. Segment(B, A) → i