Simple query related to $\cos(\theta)$ function

Question

I want to find the range of $\theta$ for which we have $$x-b\cos(\theta)<0$$ where $x<b$ and $b$ is a constant and both can have only positive values. I can write the above inequality as follows $$\arccos\left(\frac{x}{b}\right)<\theta.$$ But $\theta=0$ does not come out in the answer although $\theta=0$ can obeys the first inequality. Where am I wrong in this?