- Given $x=r\cos\theta$ and $y=r\sin\theta$. Compute both $dx$ and $dy$ in terms of $r$, $\theta$, $dr$ and $d\theta$. (If you need to, assume that everything depends on $t$, compute derivatives, then then multiply by $dt$.) Rewrite as a vector and matrix equations (see the board).
- Plot the curve $r=3-3\sin\theta$. [Hint: Make an $(r,\theta)$ table, but pick values for $\theta$ that result in integer values for $r$.)
- Plot the curve $r=2\cos3\theta$.
- Plot the curve $r=4\cos\theta$.
- For the curve $r=3-3\sin\theta$, first find $dr$ in terms of $\theta$ and $d\theta$. Then state both $dx$ and $dy$ at $\theta = \pi/2$.
- Give a vector equation of the tangent line to the curve above at $\theta=\pi/2$.
- Cartesian equation of the tangent line to the curve at $\theta=\pi/2$.
- Repeat the last 3 problems with the curve from part 2 at $t=\pi/6$, and then the curve from part 3 at $t=\pi$.
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