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Degree to Radian Conversion Example

Degree to Radian Conversion Example
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2014-05-13 20:32
AngleFunctionTrigonometry
In collections CCGPS AA Unit 5 Lesson 1
This example demonstrates how to convert 78 degrees to radians, showing both the exact and decimal approximations. It involves core math concepts like angle unit conversion and basic trigonometric formulas. The construction uses GeoGebra commands/objects such as LaTeX, GCD, stepMax, stepper, steps, counter, text elements, angleDeg, angleRad, and buttons. Suitable for high school students learning about angle-radian relationships.

GeoGebra Commands & Parameters

  1. LaTeX(steps) → counter
  2. LaTeX("\text{Determine which conversion factor to use.}") → text1
  3. LaTeX("\text{Set up the multiplication.}") → text4
  4. LaTeX("\text{Multiply, and cancel out the degree symbols.}") → text6
  5. LaTeX((("\textcolor{#000099}{\frac{" * angleDeg) * "\pi}{180}}")) → text7
  6. GCD(angleDeg, 180) → gcf
  7. LaTeX("\text{Use your calculator to find the measure of the angle as a decimal.}") → text10
  8. LaTeX((((((("\textcolor{#000099}{\frac{" * numer) * "\pi}{") * denom) * "}\approx") * angleRad) * "}")) → text11
  9. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → text14
  10. LaTeX((("\text{Convert " * angleDeg) * "° to radians.}")) → Problem
  11. LaTeX((("\text{Multiply " * angleDeg) * "° by the conversion factor.}")) → text3
  12. LaTeX((((("\text{Converted to radians, the decimal measure of " * angleDeg) * "° is}\cr\text{approximately ") * angleRad) * " radians.}")) → text12
  13. LaTeX((((("\text{Recall that radians compare the value of the arc length to the value of}\cr\text{the radius; therefore, for this " * angleDeg) * "° angle, the arc length is approximately}\cr\text{") * angleRad) * " times the length of the radius.}")) → text13
  14. LaTeX("\text{Reduce the fraction, if possible.}") → text8
  15. LaTeX("\text{Recall that }\pi\text{ radians = 180°. Thus, }\frac{\pi\text{ }radians}{180°}\text{ = 1, since dividing}\cr\text{one quantity by its equivalent is equal to 1. Since degrees need to be}\cr\text{converted to radians, multiply by }\frac{\pi}{180°}\text{ so that the degrees in the}\cr\text{denominator will cancel out and radians will remain.}") → text2
  16. LaTeX((((((((((("\text{The greatest common factor of }\textcolor{#000099}{" * angleDeg) * "}\text{ and }\textcolor{#000099}{180}\text{ is }\textcolor{#000099}{") * gcf) * "}\text{, so the reduced}\cr\text{form of the exact measure of }\textcolor{#000099}{") * angleDeg) * "°}\text{ in radians is }\textcolor{#000099}{\frac{") * numer) * "\pi}{") * denom) * "}}.")) → text9
  17. LaTeX((("\textcolor{#000099}{" * angleDeg) * "^{\circ}\bullet\frac{\pi}{180^{\circ}}}")) → text5

AI Drawing Prompt Reference

Create a math illustration showing the conversion of 78 degrees to radians. Include text steps like 'Determine the conversion factor,' 'Set up multiplication,' and 'Multiply and cancel degree symbols.' Display the exact radian value using π and the decimal approximation. Show the angle unit conversion formula, with buttons to return to the original problem or generate a similar one. Note that π radians equals 180 degrees and explain the relationship between arc length and radius.
The prompt above was compiled from the original drawing commands and is for reference only.