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Trigonometric Functions in Rectangular and Polar Coordinates

Trigonometric Functions in Rectangular and Polar Coordinates
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2015-01-24 04:22
FunctionTrigonometryGraphing
This example demonstrates the graphs of trigonometric functions in rectangular and polar coordinates. By dragging the rectangular curve, you can observe its changes in both coordinate systems. Key mathematical concepts include trigonometric functions, rectangular coordinates, and polar coordinates. Commands used include CurveCartesian, Sequence, If, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Textfield(r) → inputBox1
  2. Line((0, 0), (1, 0)) → HorizAxis
  3. Line((0, 0), (0, 1)) → VertAxis
  4. Sequence(Line[(a, 0), (a, 1)], a, 0, 6.28319, 0.5235987755982988) → VerticalLines
  5. Sequence(Circle[(12.5, 0), k], k, 1, 6) → polarCircles
  6. Sequence(Segment[(((-6) * cos(a)) + 12.5, ((-6) * sin(a))), ((6 * cos(a)) + 12.5, (6 * sin(a)))], a, 0, 2.87979, 0.2618) → radialLines
  7. Sequence(Segment[(0, a), (6.3, a)], a, -6, 6) → HorizontalLines
  8. Line((12.5, 0), (12.5, 1)) → v_2
  9. If(a_2, RectAngle, PolarAngle) → PAM
  10. If(a_2, PAM = RectAngle, PAM = PolarAngle) → b
  11. CurveCartesian((r(t) * cos(t)) + 12.5, (r(t) * sin(t)), t, 0, 6.283185307179586) → a
  12. CurveCartesian((r(t) * cos(t)) + 12.5, (r(t) * sin(t)), t, 0, Min[1.5707963267948966, PAM]) → a1
  13. CurveCartesian((r(t) * cos(t)) + 12.5, (r(t) * sin(t)), t, 1.5707963267948966, Min[3.141592653589793, PAM]) → a2
  14. CurveCartesian((r(t) * cos(t)) + 12.5, (r(t) * sin(t)), t, 3.141592653589793, Min[4.71238898038469, PAM]) → a3
  15. CurveCartesian((r(t) * cos(t)) + 12.5, (r(t) * sin(t)), t, 4.71238898038469, Min[6.283185307179586, PAM]) → a4