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Writing Sine and Cosine Functions with Amplitude and Vertical Shift Changes

Writing Sine and Cosine Functions with Amplitude and Vertical Shift Changes
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2017-10-20 22:49
FunctionTrigonometrySlider Animation
This example demonstrates how to write sine and cosine functions based on changes in amplitude and vertical shift. Key mathematical concepts include sine and cosine functions and their parameter variations. Using GeoGebra commands such as Sequence, Union, and RandomElement, the function graph can be dynamically adjusted. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(i, i, -10, -1 / 2, 0.5) → L_1, {-10, -9.5, -9, -8.5, -8, -7.5, -7, -6.5, -6, -5.5, -5, -4.5, -4, -3.5, -3, -2.5, -2, -1.5, -1, -0.5}
  2. Sequence(i, i, 1 / 2, 10, 1 / 2) → L_2, {0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10}
  3. Union(L_1, L_2) → L_3
  4. Sequence(i, i, -10, 10, 1 / 2) → dlist, {-10, -9.5, -9, -8.5, -8, -7.5, -7, -6.5, -6, -5.5, -5, -4.5, -4, -3.5, -3, -2.5, -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10}
  5. RandomElement(dlist) → d
  6. RandomElement(L_3) → a
  7. Random(1, 2) → n
  8. Textfield(h) → InputBox1
  9. If(n ≟ 1, abs(y(A) - y(C)), abs(y(B) - y(D))) → b

AI Drawing Prompt Reference

Draw a sine function and a cosine function graph with variable amplitude and vertical shift. First, create a sequence from -10 to 10 with a step of 0.5, then randomly select an amplitude value and a vertical shift value. Based on these values, draw the sine and cosine function graphs and display their amplitude and vertical shift changes.
The prompt above was compiled from the original drawing commands and is for reference only.