Same Root Sine Curves
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This example demonstrates sine curves with the same roots. It involves core concepts of trigonometry and linear equations. By adjusting parameters, one can observe the intersection points of different sine curves. This construction uses function commands and is suitable for high school mathematics education and learning.
GeoGebra Commands & Parameters
f(x) = sin(x)g(x) = (2 * sin(x))h(x) = (3 * sin(x))j(x) = (4 * sin(x))k(x) = (-sin(x))m(x) = sin(x + π)n(x) = sin(x - π)l(x) = sin((0.5 * x))p(x) = sin((2 * x))q(x) = 1 + sin(x - π / 2)r(x) = -1 + sin((2 * x) + ((5 * π)) / 2)
AI Drawing Prompt Reference
Draw a set of sine curves that share the same roots. Start with the basic sine curve, then add sine curves with amplitudes of 2, 3, and 4 times, plus one with negative amplitude. Next, include sine curves shifted by π and -π in phase. Then add curves with periods doubled and halved. Finally, add two vertically shifted sine curves: one shifted up by 1 unit and right by π/2, and another shifted down by 1 unit with adjusted phase. All curves intersect the x-axis at the same points, illustrating how different parameters affect the sine function.
The prompt above was compiled from the original drawing commands and is for reference only.