GATE 2023 MN – Question 21
For $x=r\cos\theta$ and $y=r\sin\theta$, find $\partial(x,y)/\partial(r,\theta)$.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (D) $r$
Explanation
The derivative matrix is $\begin{pmatrix}\cos\theta&-r\sin\theta\\\sin\theta&r\cos\theta\end{pmatrix}$. Its determinant is r cos²θ+r sin²θ = r, so D. The coordinate-area factor is r, not r².