Convert the polar point \((r,\theta)=(2,\pi/3)\) to Cartesian coordinates.

Convert the Cartesian point \((3,4)\) to polar coordinates with \(r>0\) and \(0<\theta<\pi/2\).

Rewrite \(x^2+y^2=16\) in polar coordinates.

Rewrite the Cartesian equation \(y=x\) in polar coordinates.

State the Jacobian factor \(dA\) when changing from Cartesian coordinates to polar coordinates.

Describe the polar bounds for the annulus \(1\le x^2+y^2\le 9\).

Convert \(\int_0^1\int_0^{\sqrt{1-x^2}} f(x,y)\,dy\,dx\) to polar coordinates.

For the change of variables \(u=x+y\), \(v=x-y\), solve for \(x\) and \(y\) in terms of \(u\) and \(v\).

Find the Jacobian \(\left|\frac{\partial(x,y)}{\partial(u,v)}\right|\) for \(x=u+v\), \(y=u-v\).

Use polar coordinates to evaluate \(\iint_R (x^2+y^2)\,dA\), where \(R\) is the disk \(x^2+y^2\le 1\).