Let \(f(x)=\frac{\sin^4 x}{4}-\frac{\sin^6x}{6}\) and \(g(x)=\frac{\cos^6 x}{6}-\frac{\cos^4x}{4}\). How many numbers are there in the set \(\{f(x)-g(x): x\in \mathbb R\}\) (if infinite, just say infinite many elements)?

**The answer**: See the picture attached. Flipped for a good reason...