Thus, in polar coordinates: [ dx , dy = r , dr , d\theta ]

. [ J = \beginbmatrix \cos \theta & -r \sin \theta \ \sin \theta & r \cos \theta \endbmatrix ]

. [ \det(J) = (\cos \theta)(r \cos \theta) - (-r \sin \theta)(\sin \theta) ] [ = r \cos^2 \theta + r \sin^2 \theta = r (\cos^2 \theta + \sin^2 \theta) = r ]

Lesson 16 - Part 1 -jac- ◆ (HOT)

Thus, in polar coordinates: [ dx , dy = r , dr , d\theta ]

. [ J = \beginbmatrix \cos \theta & -r \sin \theta \ \sin \theta & r \cos \theta \endbmatrix ] Lesson 16 - Part 1 -Jac-

. [ \det(J) = (\cos \theta)(r \cos \theta) - (-r \sin \theta)(\sin \theta) ] [ = r \cos^2 \theta + r \sin^2 \theta = r (\cos^2 \theta + \sin^2 \theta) = r ] Thus, in polar coordinates: [ dx , dy = r , dr , d\theta ]