Hi,

I'm having trouble with an assignment of mine. I hope someone here can help me. It should be trivial - I just think I've overseen something... Well, here goes:

I have a mapping $\displaystyle \theta : \mathbb{R}^2 \setminus \{ (x,y) | y = 0, x \leq 0 \} \rightarrow (-\pi,\pi)$ defined such that $\displaystyle \frac{x}{\sqrt{x^2 + y^2}} = \cos\theta(x,y)$ and $\displaystyle \frac{y}{\sqrt{x^2 + y^2}} = \sin\theta(x,y)$. So, it is the angle between the x-axis and the line connecting origo and the point $\displaystyle (x,y)$.

How do I show that the mapping $\displaystyle \theta(x,y)$ isnotcontinous on the negative x-axis?