When is $a^2 + b^2 + c^2 > ac\cos{x} + bc\sin{x}$? I was hoping someone could help me with finding the values of $a$, $b$, $c$ and $x$ for which the following inequation is true: $$a^2 + b^2 + c^2 > ac\cos{x} + bc\sin{x}$$
where $a$, $b$ and $c$ are real numbers and $0 \le x < 2\pi.$ 
I don't really know how to start and I think this problem is more complicated than it looks.
Thank you very much for reading.

By C-S and AM-GM we obtain:
$$ac\cos{x}+bc\sin{x}\leq\sqrt{(a^2c^2+b^2c^2)(\cos^2x+\sin^2x)}=\sqrt{(a^2+b^2)c^2}\leq$$
$$\leq\frac{1}{2}(a^2+b^2+c^2)\leq a^2+b^2+c^2.$$
The equality occurs for $a=b=c=0$, which gives the answer:
$$\{(a,b,c,x)|a^2+b^2+c^2\neq0\}$$
