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Sailboat and Periodic Functions

Sailboat and Periodic Functions
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2016-05-18 03:23
FunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Sail Away!
This example uses a sailboat near a dock to help students understand periodic functions. By adjusting the sailboat's height, students can see the wave-like changes in periodic functions. It involves trigonometry and coordinate geometry, using objects and commands like circle, polygon, and locus. Suitable for high school math education.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Segment(D, C) → g
  4. Segment(C, A) → h
  5. Polygon(E, F, G, H) → poly1, e, f_1, g_1, h_1
  6. Point(g_1) → I
  7. Polygon(I, J, K, L) → poly2, i, j, k, l
  8. Intersect(g_1, yAxis) → M
  9. Point(g_1) → P
  10. Polygon(M, N, O, P) → poly3, m, n, o, p
  11. Polygon(T, S, Q, R) → poly4, t, s, q, r
  12. Polygon(U, W, Z, A_1, V) → poly5, b, d, i_1, j_1, k_1
  13. Circle(B_1, C_1) → c_1
  14. Circle(B_1, D_1) → d_1

AI Drawing Prompt Reference

Draw a geometric figure related to a sailboat and periodic functions. Start with a circle and place a point on it; connect this point to the center and to another fixed point with segments. Construct a quadrilateral, then pick a point on one of its sides and form another quadrilateral with that point and three other points. Let one quadrilateral intersect the vertical axis, and choose a point on its side to build a third quadrilateral. Then draw two more quadrilaterals and a pentagon. Finally, draw two circles with different centers to suggest waves and the sailboat, illustrating periodic changes.
The prompt above was compiled from the original drawing commands and is for reference only.