Sine Function Period Calculation Example

GeoGebra Commands & Parameters

1. LaTeX(steps) → counter
2. LaTeX("\text{Identify the period of }\textcolor{#000099}{g(x).}") → text1
3. LaTeX("\text{This will be needed to calculate the number of complete cycles of }\textcolor{#000099}{g(x)}\text{ that}\cr\text{exist in the restricted domain.}") → text2
4. FractionText(permult) → permulttext
5. LaTeX((((("\text{The period of the function }\textcolor{#000099}{g(x) = " * g) * "}\text{ is }\textcolor{#000099}{") * permulttext) * "\pi}.")) → text5
6. FractionText(dlrad) → dlradtext
7. FractionText(drrad) → drradtext
8. If(toggle ≟ 1, LaTeX[(("\text{The period of }\textcolor{#000099}{g(x)}\text{, converted to degrees, is }\textcolor{#000099}{" * perdeg) * "^{\circ}}.")], LaTeX[(((("\text{The domain of }\textcolor{#000099}{g(x)}\text{, converted to radians, is }\textcolor{#000099}{\left[" * dlradtext) * "\pi,") * drradtext) * "\pi\right]}.")]) → text9
9. If(toggle ≟ 1, LaTeX["\text{In order to determine the number of completed cycles, calculate the total}\cr \text{number of degrees within the domain of the function, and then divide this}\cr\text{number by the period measured in degrees.}"], LaTeX["\text{In order to determine the number of completed cycles, calculate the total}\cr \text{number of radians within the domain of the function, and then divide this}\cr\text{number by the period measured in radians.}"]) → text11
10. LaTeX("\text{Domain:}") → text12
11. LaTeX("\text{Period:}") → text14
12. LaTeX("\frac{Domain}{Period}:") → text16
13. If(toggle ≟ 1, LaTeX[(((((("\textcolor{#000099}{" * dr) * "^{\circ}-\left(") * dl) * "^{\circ}\right)=") * domdeg) * "^{\circ}}")], LaTeX[(((((("\textcolor{#000099}{" * drradtext) * "\pi-\left(") * dlradtext) * "\pi\right)=") * domrad) * "\pi}")]) → text13
14. If(toggle ≟ 1, LaTeX[(("\textcolor{#000099}{" * perdeg) * "^{\circ}}")], LaTeX[(("\textcolor{#000099}{" * permulttext) * "\pi}")]) → text15
15. LaTeX("\text{Verify the result by graphing.}") → text19
16. If(toggle ≟ 1, dl - perdeg / 4, ((dlrad - permult / 4) * π)) → xmin
17. If(toggle ≟ 1, dr + perdeg / 4, ((drrad + permult / 4) * π)) → xmax
18. Min(0 - a / 4, c - a - a / 4) → ymin
19. Max(0 + a / 4, c + a + a / 4) → ymax
20. LaTeX((((((((("\text{The number of complete cycles of }\textcolor{#000099}{g(x)=" * g) * "}\text{ on the}\cr\text{restricted domain }\textcolor{#000099}{[") * dl) * "^{\circ},") * dr) * "^{\circ}]}\text{ is }\textcolor{#000099}{") * fullper) * "}.")) → text18
21. If(toggle ≟ 1, Sequence[(dl + (n * perdeg), fplotdeg(dl + (n * perdeg))), n, 0, fullper, 1], Sequence[(((dlrad + (n * permult)) * π), fplotrad(((dlrad + (n * permult)) * π))), n, 0, fullper, 1]) → list1
22. Sequence(Vector[Element[list1, n], Element[list1, n + 1]], n, 1, Length[list1] - 1) → list2
23. LaTeX((((((("\textcolor{#000099}{g(x)=" * g) * "}\text{ on }\textcolor{#000099}{\left[") * dl) * "^{\circ},") * dr) * "^{\circ}\right]}")) → Problem
24. LaTeX("\text{Convert the period to degrees or convert the domain to radians.}") → text6
25. If(toggle ≟ 1, LaTeX["\text{Converting period to degrees}"], LaTeX["\text{Converting domain to radians}"]) → toggleText
26. LaTeX("\text{Since the domain is given in degrees and the period is found in radians, one}\cr\text{or the other must be converted so that the units match before any comparison can be made.}") → text7
27. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → text20
28. If(toggle ≟ 1, LaTeX[(((((("\textcolor{#000099}{\text{Greatest integer less than or equal to }\left(\frac{" * domdeg) * "^{\circ}}{") * perdeg) * "^{\circ}}\right)=") * fullper) * "}")], LaTeX[(((((("\textcolor{#000099}{\text{Greatest integer less than or equal to }\left(\frac{" * domrad) * "\pi}{") * permult) * "\pi}\right)=") * fullper) * "}")]) → text17
29. LaTeX("\text{Set the argument of the function equal to the period of the parent sine}\cr\text{function, }\textcolor{#000099}{\sin(x)}\text{, and solve for }\textcolor{#000099}{x}.") → text3
30. LaTeX((((("\text{Determine the number of complete cycles }\textcolor{#000099}{g(x)}\text{ makes over the domain }\textcolor{#000099}{[" * dl) * "^{\circ}, ") * dr) * "^{\circ}]}.")) → text10
31. If(toggle ≟ 1, LaTeX[(((((("\textcolor{#000099}{1}\text{ radian}\textcolor{#000099}{=\frac{180^{\circ}}{\pi}}\text{, so }\textcolor{#000099}{" * permulttext) * "\pi}\text{ radians is }\textcolor{#000099}{") * permulttext) * "\pi\cdot\frac{180^{\circ}}{\pi}=") * perdeg) * "^{\circ}}.")], LaTeX[(((((((((("\textcolor{#000099}{1^{\circ}=\frac{\pi\text{ radians}}{180}}\text{, so }\cr \textcolor{#000099}{" * dl) * "^{\circ}}\text{ is }\textcolor{#000099}{") * dl) * "^{\circ}\frac{\pi}{180^{\circ}}=") * dlradtext) * "\pi}\cr \text{and}\cr \textcolor{#000099}{") * dr) * "^{\circ}\frac{\pi}{180^{\circ}}=") * drradtext) * "\pi}.")]) → text8
32. TableText({{LaTeX[(("\textcolor{#000099}{" * b) * "x = 2\pi}")], LaTeX["\text{Set the argument equal to the period of }\textcolor{#000099}{\sin(x)}."]}, {LaTeX[(("\textcolor{#000099}{x = \frac{2}{" * b) * "}\pi}")], LaTeX["\text{Solve for }\textcolor{#000099}{x}."]}, {LaTeX[(("\textcolor{#000099}{x = " * permulttext) * "\pi}")], LaTeX["\text{Simplify.}"]}}) → text4