Sine Function Equation Construction

GeoGebra Commands & Parameters

1. LaTeX(steps) → counter
2. LaTeX("\text{Determine the value of a.}") → text1
3. LaTeX("\text{The variable a represents the amplitude of the function,}\cr\text{or how far the function rises above its midline.}") → text2
4. LaTeX((((("\text{Since the function rises " * amp) * " units above its midline, its amplitude is ") * amp) * ".}")) → text3
5. LaTeX((("\text{The value of a, the amplitude, is " * amp) * ".}")) → text4
6. LaTeX("\text{Determine the value of b.}") → text5
7. LaTeX("\text{Substitute this value into the formula for the period and solve for b.}") → text8
8. LaTeX((("\text{The value of b is }" * bmult) * "\pi.")) → text10
9. LaTeX("\text{Determine the value of c.}") → text11
10. LaTeX("\text{Determine the value of d.}") → text13
11. LaTeX("\text{The variable d gives the vertical shift. }") → text14
12. If(midline < 0, "down", If[midline > 0, "up", ""]) → direction
13. LaTeX("\text{Substitute a, b, c, and d into the general form of the sine function.}") → text16
14. Simplify((amp * sin(((bmult * π) * (x - xshift)))) + midline) → f
15. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → text19
16. LaTeX((((((((("\text{horizontal shift = }" * xshift) * "\cr\text{frequency = }") * freq) * "\cr\text{rise above midline= }") * amp) * "\cr\text{midline = }") * midline) * "")) → Problem
17. LaTeX("\text{The period (the length of one cycle of the curve) is equal to }\frac{2\pi}{b},\cr\text{and the frequency is the reciprocal of the period.}") → text6
18. LaTeX((((((("\text{The reciprocal of the given frequency, }" * freq) * "\text{, is }\frac{1}{") * freq) * "}\text{. Thus, }\frac{1}{") * freq) * "}\text{ is the period.}")) → text7
19. LaTeX((((((((((("\text{Since the function’s midline is y = " * midline) * ", this means that the entire}\cr\text{function has been shifted ") * direction) * " ") * abs(midline)) * " unit } (") * midline) * ")\text{, so d = }") * midline) * ".")) → text15
20. TableText({{LaTeX["f(x) = a \sin[b(x – c)] + d"], LaTeX["\text{General form of the sine function}"]}, {LaTeX[(((((((("f(x)=(" * amp) * ")\sin\left[") * bmult) * "\pi\left(x-[") * xshift) * "]\right)\right]+(") * midline) * ")")], LaTeX["\text{Substitute.}"]}, {LaTeX[("f(x)=" * f)], LaTeX["\text{Simplify.}"]}}) → text17
21. LaTeX((("\text{The equation of the function is f(x) = }" * f) * ".")) → text18
22. LaTeX((((("\text{The variable c gives the horizontal shift. }\cr\text{Since the horizontal shift is }" * xshift) * "\text{, c = }") * xshift) * ".")) → text12
23. TableText({{LaTeX["\text{period}=\frac{2\pi}{b}"], LaTeX["\text{Formula for the period}"]}, {LaTeX[(("\frac{1}{" * freq) * "}=\frac{2\pi}{b}")], LaTeX[(("\text{Substitute }\frac{1}{" * freq) * "}\text{ for the period.}")]}, {LaTeX[(("b=" * freq) * "(2\pi)")], LaTeX["\text{Cross multiply to eliminate the fractions.}"]}, {LaTeX[(("b=" * bmult) * "\pi")], LaTeX["\text{Multiply.}"]}}) → text9