MathPlotAI Logo MathPlotAI

Graphs of Sine and Cosine Functions by Ken Schwartz

Graphs of Sine and Cosine Functions by Ken Schwartz
Loading the math board and drawing, please wait…
2016-01-26 11:54
FunctionTrigonometryCoordinate GeometryGeometric ConstructionGraphing
This example demonstrates the connection between the unit circle and the graphs of sin(x) and cos(x). It involves core math concepts like the unit circle, trigonometric functions, and coordinate geometry. Constructed using GeoGebra commands such as Segment, Intersect, Circle, Vector, Line, and Angle, with objects like Θ, segSin, segCos, Ps, s, Pr, c, uc, vecSin, vecSin2, vecCos2, Pc, vecCos, xa, cx, cy, chkSin, chkCos, e, segRadius, txtX, txtY, txtPos1, txtZero, txtNeg1, txtRad, txtDeg, txtCos, txtSin, segCosCon1, segCosCon2, segSinCon, α. Suitable for high school mathematics education to understand the relationship between trigonometric function graphs and the unit circle.

GeoGebra Commands & Parameters

  1. Segment((-1, sin(Θ)), (1, sin(Θ))) → segSin
  2. Segment((cos(Θ), -1), (cos(Θ), 1)) → segCos
  3. Intersect(segSin, segCos) → Pr
  4. Circle((0, 0), 1) → uc
  5. Vector((1.5 + Θ / 2, 0), (1.5 + Θ / 2, sin(Θ))) → vecSin
  6. Vector((1, 0), (1, sin(Θ))) → vecSin2
  7. Vector((0, 1), (cos(Θ), 1)) → vecCos2
  8. Vector((1.5 + Θ / 2, 0), (1.5 + Θ / 2, cos(Θ))) → vecCos
  9. Segment((1.3, 0), (4.841592653589793, 0)) → xa
  10. Segment((-1.1, 0), (1.1, 0)) → cx
  11. Segment((0, -1.1), (0, 1.1)) → cy
  12. Line((Θ / 2 + 1.5, 0), (Θ / 2 + 1.5, 1)) → e
  13. Segment((0, 0), (cos(Θ), sin(Θ))) → segRadius
  14. Segment((cos(Θ), 1), (1.5 + Θ / 2, 1)) → segCosCon1
  15. Segment((1.5 + Θ / 2, 1), (1.5 + Θ / 2, cos(Θ))) → segCosCon2
  16. Segment((1, sin(Θ)), (1.5 + Θ / 2, sin(Θ))) → segSinCon
  17. Angle(cx, segRadius) → α

AI Drawing Prompt Reference

Draw a unit circle with an angle Θ marked on it. Connect the center to the point on the circle to form a radius, and project this point onto the x-axis to create vertical lines reaching the values of sin(Θ) and cos(Θ). Around the unit circle, plot the graphs of sin(Θ) and cos(Θ), and use vectors to show the transition from the angle's terminal side to the corresponding function values. Mark the positions of +1 and -1 on the x-axis, and add auxiliary lines to connect the function graphs to the axes, clearly illustrating the relationship between trigonometric functions and the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.