I used to have a car with a very aggressive horn and never wanted to use it because it did sound like I was cussing something out. I couldn't get the light "beep beep" of communication, only the FUCK OFF ASSHOLE honk.
Now you have a different car and can use the horn as a communication by short tap tap.
But the wave is the apology. I have had people accidentally cut me off and when I swerve to pass have gotten a wave and mouthed sorry.