Hints

• The Scheme functions, sin, and cos, take arguments in radians, but the Plumbing Graphics function, bend, takes its argument in degrees. Degrees can be converted to radians by multiplying by $\frac{2\pi}{360}$.

• The Scheme function, random, takes an integer as argument and returns a random number between $0$ and $n-1$.

• Write a tail-recursive function, ecoli-it, which takes $x_{t-1}$, $y_{t-1}$, $d_{t-1}$, $\theta_{t-1}$ and a graphics object, $g_{t-1}$, representing the trajectory of the bacterium from start to $t-1$ and returns a graphics object representing the trajectory of the bacterium from start to finish.