I am trying to convert dxdy in cartesian into polar plane.
and have to prove: dxdy = rd dr
Here is my conversion proof:
x = rcos
y = rsin
dx = -rsin d + cos dr
dy = rcos d + sin dr
ignoring 2nd order differentials, and keeping only drd ,
dxdy = -rsin d sin dr
+ rcos drcos d
= rd dr(-sin + cos )
I need to equate (-sin + cos ) = 1,
but i can't because of the -ve sign. Where did I go wrong?
Thanks for your time.