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Reciprocal Trig Ratios

Reciprocal Trig Ratios
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2019-02-06 00:08
AngleFunctionTrigonometry
This example demonstrates the concept of reciprocal trigonometric ratios. It constructs angles and trigonometric values to help students understand the properties of cosecant, secant, and other reciprocal ratios. It uses commands like Sequence, Zip, Point, and others, suitable for high school math education.

GeoGebra Commands & Parameters

  1. Sequence(i, i, 0, 357, 3) → angleMeasures
  2. Zip(((5 * cos(A°)), (5 * sin(A°))), A, angleMeasures) → pointList
  3. Point(pointList) → P
  4. IndexOf(P, pointList) → currIndx
  5. If(x(P) ≠ 0, 5 / x(P)) → D4
  6. UnicodeToLetter(10007) → xmark
  7. UnicodeToLetter(10003) → cmark
  8. Segment(P, (x(P), 0)) → VerticalLine
  9. Vector((0, 0), (qWidth, 0)) → hAxis
  10. Rotate(hAxis, π, (0, 0)) → hAxis2
  11. Rotate(hAxis, π / 2, (0, 0)) → vAxis
  12. Rotate(hAxis, (3 * π / 2), (0, 0)) → vAxis2
  13. Element(angleMeasures, currIndx) → currAngle
  14. Zip(Rotate[A, currAngle°, (0, 0)], A, {(1.8, -0.2), (2, 0), (2.2, -0.2)}) → chevronPoints
  15. Sequence(Segment[Element[chevronPoints, i], Element[chevronPoints, i + 1]], i, 1, 2) → chevron
  16. If((5 / y(P) * 100) ≟ (round(5 / y(P), 2) * 100), " = ", " \approx ") → cscEquality
  17. If(y(P) ≟ 0, "\text{undefined}", (("\(" * 5 / y(P)) * "\)")) → cscFinalFmt
  18. LaTeX(((((("\text{\csc(\theta) = \dfrac{\(r\)}{\(y\)} = \dfrac{\(5\)}{\(" * y(P)) * "\)}") * cscEquality) * cscFinalFmt) * "}")) → cscStr
  19. If((5 / x(P) * 100) ≟ (round(5 / x(P), 2) * 100), " = ", " \approx ") → secEquality
  20. If(x(P) ≟ 0, "\text{undefined}", (("\(" * 5 / x(P)) * "\)")) → secFinalFmt
  21. LaTeX(((((("\text{\sec(\theta) = \dfrac{\(r\)}{\(x\)} = \dfrac{\(5\)}{\(" * x(P)) * "\)}") * secEquality) * secFinalFmt) * "}")) → secStr
  22. If((x(P) / y(P) * 100) ≟ (round(x(P) / y(P), 2) * 100), " = ", " \approx ") → cotEquality
  23. If(y(P) ≟ 0, "\text{undefined}", (("\(" * x(P) / y(P)) * "\)")) → cotFinalFmt
  24. LaTeX(((((((("\text{\cot(\theta) = \dfrac{\(x\)}{\(y\)} = \dfrac{\(" * x(P)) * "\)}{\(") * y(P)) * "\)}") * cotEquality) * cotFinalFmt) * "}")) → cotStr
  25. TableText({{thetaStr, rStr, cscStr, secStr, cotStr}}, "vl") → displayData
  26. CurveCartesian((2 * cos(((2 * π) * t))), (2 * sin(((2 * π) * t))), t, 0, currAngle / 360) → angleCurve
  27. Polygon({(0, 0), (0, 0.5), (0.5, 0.5), (0.5, 0)}) → angleBoxTemplate
  28. Element(angleMeasures, currIndx) → test
  29. Translate(angleBoxTemplate, (If[x(P) > 0, x(P) - 0.5, x(P)], If[y(P) < 0, -0.5, 0])) → angleBox