- Plot the curve $r=3-3\sin\theta$ in the $xy$ plane. [Hint: Make an $(r,\theta)$ table, but pick values for $\theta$ that make $\sin$ easy to compute.]
- For the curve above, first compute $dr$ in terms of $\theta$ and $d\theta$. Then compute both $dx$ and $dy$ in terms of $d\theta$ at $\theta = \pi$. (Remember $x=r\cos\theta$ which gives $dx = \cos\theta dr -r\sin\theta d\theta$. Substitute to find $dx$ in terms of $d\theta$.)
- Give a vector equation of the tangent line to the curve above at $\theta=\pi$, then give a cartesian equation using point-slope form.
- Repeat the last 3 problems with the curve $r=2\cos3\theta$ at $t=\pi/6$.
- Repeat the last 3 problems with the curve $r=3\cos\theta$ at $t=\pi/4$.
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