Reference Angle Calculation Example

GeoGebra Commands & Parameters

1. LaTeX(steps) → counter
2. Circle((0, 0), 1) → c
3. LaTeX("\text{0 radians}") → zero
4. Segment((0, 0), C) → a
5. Segment((0, 0), (1, 0)) → b
6. Angle(A, (0, 0), C) → α
7. If(0 < factor ≤ 0.5, LaTeX["\text{I}"], If[0.5 < factor ≤ 1, LaTeX["\text{II}"], If[1 < factor ≤ 1.5, LaTeX["\text{III}"], LaTeX["\text{IV}"]]]) → quadrant
8. If(0 < factor ≤ 0.5, LaTeX["\text{The measure of the original angle is the measure of the reference angle.}"], If[0.5 < factor ≤ 1, LaTeX["\text{Subtract the measure of the original angle from π radians to find the }\cr\text{measure of the reference angle.}"], If[1 < factor ≤ 1.5, LaTeX["\text{Subtract π radians from the original angle measure to find the}\cr\text{measure of the reference angle.}"], LaTeX["\text{Subtract the measure of the original angle from 2π radians to find the }\cr\text{measure of the reference angle.}"]]]) → subtraction
9. If(0 < factor ≤ 0.5, Angle[A, (0, 0), C], If[0.5 < factor ≤ 1, Angle[C, (0, 0), B], If[1 < factor ≤ 1.5, Angle[B, (0, 0), C], Angle[C, (0, 0), A]]]) → ref
10. If(0 < factor ≤ 0.5, angle, If[0.5 < factor ≤ 1, π - angle, If[1 < factor ≤ 1.5, angle - π, (2 * π) - angle]]) → refang
11. LaTeX("\text{Move the slider to solve the problem.}") → text0
12. LaTeX("\text{Sketch a unit circle, and then label π radians and 2π radians.}") → text1
13. LaTeX("\text{A half rotation (180°) is π radians and a full rotation (360°) is 2π radians. }\cr\text{Notice that 0 radians and 2π radians are in the same location on the unit circle, }\cr\text{but represent different angle measures.}") → text2
14. LaTeX("\text{Determine the measure of the angle between the terminal side and the x-axis. }") → text5
15. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → text9
16. LaTeX((("\text{The terminal side is in Quadrant }" * quadrant) * ".")) → text10
17. LaTeX((((("\text{The terminal side falls in Quadrant } " * quadrant) * ".\cr") * subtraction) * "")) → text6
18. If(0 < factor ≤ 0.5, LaTeX[(("\textcolor{#CC0000}{" * angle) * "\text{ radian(s)}}")], If[0.5 < factor ≤ 1, LaTeX[(((("\textcolor{#CC0000}{π-" * angle) * "=") * refang) * "\text{ radian(s)}}")], If[1 < factor ≤ 1.5, LaTeX[(((("\textcolor{#CC0000}{ " * angle) * "- π =") * refang) * "\text{ radian(s)}}")], LaTeX[(((("\textcolor{#CC0000}{ 2π -" * angle) * "=") * refang) * "\text{ radian(s)}}")]]]) → text7
19. LaTeX((("\text{To see which quadrant the terminal side lies in, rewrite the given angle,}\cr\text{" * angle) * ", in terms of π.}")) → text3
20. LaTeX((((("\textcolor{#006633}{" * angle) * " = ") * factor) * " π }")) → text4
21. LaTeX((("\text{" * angle) * " radian(s)}")) → Problem
22. LaTeX((((("\text{The reference angle for }" * angle) * "\text{ radian(s) is approximately }") * refang) * "\text{ radian(s).}")) → text8