Reference Angle Calculation

GeoGebra Commands & Parameters

1. LaTeX(steps) → counter
2. Circle((0, 0), 1) → c
3. LaTeX("\text{0 radians}") → zero
4. LaTeX("\text{Sketch the angle.}") → text3
5. If(angleNum / angleDen < 1, Sequence[i / angleDen, i, 1, angleDen - 1], Sequence[1 + i / angleDen, i, 1, angleDen - 1]) → list1
6. Zip((cos((a * π)), sin((a * π))), a, list1) → list2
7. Zip(Segment[(0, 0), a], a, list2) → list3
8. Segment((0, 0), C) → a
9. Segment((0, 0), (1, 0)) → b
10. Angle(A, (0, 0), C) → α
11. 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
12. 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
13. If(0 < factor ≤ 0.5, angleNum, If[0.5 < factor ≤ 1, angleDen - angleNum, If[1 < factor ≤ 1.5, angleNum - angleDen, (2 * angleDen) - angleNum]]) → refNum
14. 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
15. LaTeX("\text{Move the slider to solve the problem.}") → text0
16. LaTeX((((("\frac{" * angleNum) * " π }{") * angleDen) * "} radians")) → Problem
17. LaTeX("\text{Sketch a unit circle, and then label π radians and 2π radians.}") → text1
18. 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
19. LaTeX("\text{Determine the measure of the angle between the terminal side and the x-axis. }") → text5
20. LaTeX((((((((("\text{The reference angle for }\frac{" * angleNum) * "\text{ }\pi}{") * angleDen) * "}\text{ radians is }\frac{") * refNum) * "\text{ }\pi}{") * angleDen) * "}\text{ radians.}")) → text8
21. If(0 < factor ≤ 0.5, LaTeX[(((("\textcolor{#CC0000}{frac{" * refNum) * "}{") * angleDen) * "}π \text{ radians}}")], If[0.5 < factor ≤ 1, LaTeX[(((((((((((("\textcolor{#CC0000}{\frac{" * angleDen) * "}{") * angleDen) * "}π -\frac{") * angleNum) * "}{") * angleDen) * "}π =\frac{") * refNum) * "}{") * angleDen) * "}π \text{ radians}}")], If[1 < factor ≤ 1.5, LaTeX[(((((((((((("\textcolor{#CC0000}{\frac{" * angleNum) * "}{") * angleDen) * "}π -\frac{") * angleDen) * "}{") * angleDen) * "}π =\frac{") * refNum) * "}{") * angleDen) * "}π \text{ radians}}")], LaTeX[(((((((((((("\textcolor{#CC0000}{\frac{2(" * angleDen) * ")}{") * angleDen) * "}π -\frac{") * angleNum) * "}{") * angleDen) * "}π =\frac{") * refNum) * "}{") * angleDen) * "}π\text{ radians}}")]]]) → text7
22. If(angleNum / angleDen < 1, LaTeX[(((((((((((((((((("\frac{" * angleNum) * " π}{") * angleDen) * "}\text{is the same as }\frac{") * angleNum) * "}{") * angleDen) * "} π. \cr\text{In other words, the terminal side is }\frac{") * angleNum) * "}{") * angleDen) * "}\text{ of the way from 0 to π.}\cr\text{Thus, imagine the semicircle between 0 radians and π radians split into ") * angleDen) * " parts }\cr\text{and then sketch the angle }\frac{") * angleNum) * "}{") * angleDen) * "}\text{ of the way around the semicircle.}")], LaTeX[(((((((((((((((((("\frac{" * angleNum) * " π}{") * angleDen) * "}\text{is the same as }\left(1+\frac{") * newNum) * "}{") * angleDen) * "}\right) π. \cr\text{In other words, the terminal side is }\frac{") * newNum) * "}{") * angleDen) * "} \text{ of the way from π to 2π. }\cr\text{Thus, imagine the semicircle between π radians and 2π radians split into ") * angleDen) * " parts }\cr\text{and then sketch the angle }\frac{") * newNum) * "}{") * angleDen) * "}\text{ of the way around the semicircle.}")]) → text4
23. LaTeX((((("\text{The terminal side falls in Quadrant } " * quadrant) * ".\cr") * subtraction) * "")) → text6
24. LaTeX("\text{Use the buttons below to review the different angles}\cr\text{or randomly generate a similar practice problem.}") → text9