Exploring Polar Graphs

This Demonstration plots the polar graphs of r(θ) = a + b f((c θ - d) π) for various trig functions f(θ).
In case the choice is the identity, r(θ) = a + k θ, where k = b (c - d) π.
What do a, b, c and d do?

Source: Exploring Polar Graphs from the Wolfram Demonstrations Project by Steven Francis