Cosine Curve Shift Demonstration

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2013-11-09 23:05

Function Trigonometry Graphing

This example demonstrates the shift of a cosine curve, visually showing how the wave moves left or right. It involves core math concepts like trigonometric function graph transformations, function shifting, and coordinate geometry. The construction uses GeoGebra commands/objects like α, A2-A15, B2-B15, P_1-P_10, list1, A12-A14, B12-B15 for parameter control and path drawing. Suitable for high school mathematics teaching to understand function graph transformation rules and deepen the understanding of trigonometric function properties.

GeoGebra Commands & Parameters

Angle α(5.183627878423159)
Numeric A2(0.0)
Numeric A3(10.0)
2 * A3 - A2
2 * A4 - A3
2 * A5 - A4
2 * A6 - A5
2 * A7 - A6
2 * A8 - A7
2 * A9 - A8
2 * A10 - A9
cos(A3° + α)
cos(A4° + α)
cos(A5° + α)
cos(A6° + α)
cos(A7° + α)
cos(A8° + α)
cos(A9° + α)
cos(A10° + α)
cos(A11° + α)
cos(A2° + α)
(A2, B2)
(A3, B3)
(A4, B4)
(A5, B5)
(A6, B6)
(A7, B7)
(A8, B8)
(A9, B9)
(A10, B10)
(A11, B11)
{P_1, P_2, P_3, P_4, P_5, P_6, P_7, P_8, P_9, P_{10}}
2 * A11 - A10
cos(A12° + α)
2 * A12 - A11
cos(A13° + α)
2 * A13 - A12
cos(A14° + α)
2 * A14 - A13
cos(A15° + α)
2 * A15 - A14
cos(A16° + α)
2 * A16 - A15
cos(A17° + α)
2 * A17 - A16
cos(A18° + α)
2 * A18 - A17
cos(A19° + α)
2 * A19 - A18
cos(A20° + α)
2 * A20 - A19
cos(A21° + α)
2 * A21 - A20
cos(A22° + α)
2 * A22 - A21
cos(A23° + α)
2 * A23 - A22
cos(A24° + α)
2 * A24 - A23
cos(A25° + α)

AI Drawing Prompt Reference

Draw a cosine curve and demonstrate its shift by moving it left or right. Start with a standard cosine curve, then adjust angle α to observe the shift.

The prompt above was compiled from the original drawing commands and is for reference only.