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Trigonometric Ratios in Four Quadrants

Trigonometric Ratios in Four Quadrants
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2019-01-06 10:22
AngleFunctionTrigonometry
This example demonstrates the variation of trigonometric ratios in four quadrants. Key mathematical concepts include trigonometric functions, angles, and quadrants. Using GeoGebra commands such as Sequence, Zip, and Point, the relationship between angles and trigonometric ratios is dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(((3 * i))°, i, 1, 120) → angleMeasures
  2. Zip(((5 * cos(A)), (5 * sin(A))), A, angleMeasures) → pointList
  3. Point(pointList) → P
  4. IndexOf(P, pointList) → pIndx
  5. UnicodeToLetter(10007) → xmark
  6. UnicodeToLetter(10003) → cmark
  7. Angle(Vector[(12, 0)], Vector[P]) → angleDisplay
  8. LaTeX("Move point \(P\) and observe the values of the trigonometric ratios.") → SpecInstruc
  9. Segment(P, (x(P), 0)) → VerticalLine
  10. If(x(P) < 0, "-", "") → cosSign
  11. Vector((0, 0), (qWidth, 0)) → hAxis
  12. Rotate(hAxis, π, (0, 0)) → hAxis2
  13. Rotate(hAxis, π / 2, (0, 0)) → vAxis
  14. Rotate(hAxis, (3 * π / 2), (0, 0)) → vAxis2
  15. Segment((0, 0), P) → terminalArm
  16. Zip(Rotate[A, Element[angleMeasures, pIndx], (0, 0)], A, {(1.8, -0.2), (2, 0), (2.2, -0.2)}) → chevronPoints
  17. Sequence(Segment[Element[chevronPoints, i], Element[chevronPoints, i + 1]], i, 1, 2) → chevron
  18. CurveCartesian((2 * cos(((2 * π) * t))), (2 * sin(((2 * π) * t))), t, 0, Element[angleMeasures, pIndx] / ((2 * π))) → angleCurve
  19. If((y(P) / 5 * 100) ≟ (round(y(P) / 5, 2) * 100), " = ", " \approx ") → sinEquality
  20. LaTeX((((("\text{\sin(\theta) = \dfrac{\(y\)}{\(r\)} = \dfrac{\(" * y(P)) * "\)}{\(5\)}}") * sinEquality) * sinFinalFmt)) → sinStr
  21. If((x(P) / 5 * 100) ≟ (round(x(P) / 5, 2) * 100), " = ", " \approx ") → cosEquality
  22. LaTeX((((("\text{\cos(\theta) = \dfrac{\(x\)}{\(r\)} = \dfrac{\(" * x(P)) * "\)}{\(5\)}}") * cosEquality) * cosFinalFmt)) → cosStr
  23. If(x(P) ≟ 0, "", If[(y(P) / x(P) * 100) ≟ (round(y(P) / x(P), 2) * 100), " = ", " \approx "]) → tanEquality
  24. If(x(P) ≟ 0, "\text{\hphantom{222}undefined}", (("\(" * y(P) / x(P)) * "\)")) → tanFinalFmt
  25. LaTeX((((((("\text{\tan(\theta) = \dfrac{\(y\)}{\(x\)} = \dfrac{\(" * y(P)) * "\)}{\(") * x(P)) * "\)}}") * tanEquality) * tanFinalFmt)) → tanStr
  26. TableText({{thetaStr, radiusStr, sinStr, cosStr, tanStr}}, "vl") → allData
  27. Polygon({(0, 0), (0, 0.5), (0.5, 0.5), (0.5, 0)}) → angleBoxTemplate
  28. Translate(angleBoxTemplate, (If[x(P) > 0, x(P) - 0.5, x(P)], If[y(P) > 0, 0, -0.5])) → angleBox