custom transformation for radius in ggplot geom_polar

Question

I'm plotting seasonal data using ggplot2. Since small values aren't visible well when I start the axis at 0 I want to offest the axis. I want the function values correspond to the area between the offset and the line, the transform for this would be r = sqrt(y+offest^2). (Correct me if I'm wrong here.)

How can I use this transformation together with geom_polar? In the following Code the Transformation does not seem to be applied:

my_function <- function(x){1+sin(x)}

my_trafo_trans <- function() trans_new("my_trafo", function(y){sign(y)*sqrt(abs(y))+1^2}, function(r){r^2+1^2})

ggplot(data=data.frame(x=0), aes(x=0)) +
  coord_trans(y = "my_trafo") +
  coord_polar(theta="x") +
  ylim(-0.5, 2 ) +
  xlim(-pi, pi) +
  stat_function(fun=my_function,  geom="line", alpha=0.75, n=1000) +
  stat_function(fun=function(x) 0, geom="line") +
  theme_bw()

Compare the output of this with the output when you comment out the coord_trans and coord_polar lines respectively.

Is it even possible to use coord_trans and coord_polar together?