Rapid Recall
- Which problems are you ready to present?
- Which problems did you sincerely attempt
- For the curve $r=2+2\sin\theta$, graph the curve in the $r\theta$ plane.
- For the curve $r=2+2\sin\theta$, graph the curve in the $xy$ plane.
- Give a vector equation of a line that passes through $(a,b)$ and is parallel to the vector $(c,d)$.
Group problems
- Plot the curve $r=3-3\cos\theta$ in both the $r\theta$ and the $xy$ plane. [Hint: Make an $(r,\theta)$ table, but pick values for $\theta$ that make $\cos$ easy to compute. Did you get a heart shaped object?]
- Plot the curve $r=3\sin2\theta$ in both the $r\theta$ and the $xy$ plane. [Hint: Make an $(r,\theta)$ table, but pick values for $\theta$ that make $\sin$ easy to compute. Did you get a clover?]
- We have already seen that $dx = \cos\theta dr-r\sin\theta d\theta$ and $dy = \sin\theta dr+r\cos\theta d\theta$. Use this information to compute the slope $dy/dx$ of the previous curve at $\theta= \pi$. [The slope is -1.]
- Give a vector equation of the tangent line to the curve in the $xy$ plane at $\theta =\pi$.
- Now swap the curve to $v=u^2$ and use the coordinates $x=2u+v$, $y=u-2v$. Then repeat the three parts above at $u=1$.
- Draw the curve in both the $uv$ and $xy$ planes.
- Find the slope $dy/dx$ at $u=1$.
- Give a vector equation of the tangent line to the curve in the $xy$ plane at $u=1$.
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