Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $f(r,\theta)=(r\cos\theta ,r\sin\theta)$ for $(r,\theta)$ $\in \mathbb R^2$ with $r\ne0$. then which are true statements?

$1$.$Df(r,\theta)$ is not zero for any $(r,\theta)$ with $r\ne0$

$2$.$Df(r,\theta)=r^2I$ for any $(r,\theta)$ with $r\ne0$

here $Df(r,\theta)$ is the matrix $$\begin{bmatrix} \cos\theta &-r \sin\theta \\ \sin\theta & r\cos\theta \end{bmatrix}$$.its determinant is $r$ which is $1$ true.but what about $2$?

Can anyone help me please .

share|cite|improve this question

1 Answer 1

For 1, consider the following: Can $$\cos \theta=\sin \theta=0?$$ For 2, consider the following example: Let $$(r,\theta)=(r,\pi).$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.