Let $f(r,\theta)=(r\cos\theta ,r\sin\theta)$ for $(r,\theta)$ $\in \mathbb R^2$ with $r\ne0$. Pick out the true statements?
1.$f$ is one-one on {$(r,\theta)\in\mathbb R^2$:$r\ne0$}
2.for any $(r,\theta)\in\mathbb R^2$ with $r\ne0$, $f$ is one-one 0n a neighborhood of $(r.\theta)$
I think Statement 1. is false since $r\ne0$, $f(r,2\pi)$=$f(r,4\pi)$ does not imply $(r,2\pi)$=$(r,4\pi)$
similar reason for 2
Am I right