Whereas before I had been more focused on where the corners of the star were, needing to scale forced me to notice how one of the edges of the star ran along x=1. This led me to restart, and after some futzing around, I managed this:
5
Expression 6: "r" equals secant left parenthesis, mod left parenthesis, theta times left parenthesis, negative 1 , right parenthesis Superscript, left parenthesis, mod left parenthesis, floor left parenthesis, StartFraction, theta Over StartNestedFraction, 2 pi NestedOver 5 , EndNestedFraction , EndFraction , right parenthesis , 2 , right parenthesis , right parenthesis , Baseline , StartFraction, 2 pi Over 5 , EndFraction , right parenthesis , right parenthesisr=secmodθ·−1modfloorθ2π5,2,2π5
00
domain \theta Minimum:
less than or equal to theta less than or equal to≤θ≤
12 pi12π
domain \theta Maximum:
6
...which I then was able to simplify to this:
7
Expression 8: "r" equals secant left parenthesis, StartAbsoluteValue, mod left parenthesis, theta , StartFraction, 4 pi Over 5 , EndFraction , right parenthesis minus StartFraction, 2 pi Over 5 , EndFraction , EndAbsoluteValue , right parenthesisr=secmodθ,4π5−2π5
00
domain \theta Minimum:
less than or equal to theta less than or equal to≤θ≤
12 pi12π
domain \theta Maximum:
8
If you're interested in hearing a longer version of my thought process, leave me a note in the comments!