20191011

• I-Learn, Problem Set, Class Pictures

Rapid Recall

1. For the curve $r=3+2\sin\theta$, graph the curve in the $r\theta$ plane.

2. For the curve $r=3+2\sin\theta$, graph the curve in the $xy$ plane.

1. Give a vector equation of a line that passes through $(a,b)$ and is parallel to the vector $(c,d)$.

Rapid Recall

1. Which problems are you ready to present?
2. Which problems did you sincerely attempt
3. For the curve $r=2+2\sin\theta$, graph the curve in the $r\theta$ plane.
4. For the curve $r=2+2\sin\theta$, graph the curve in the $xy$ plane.
5. Give a vector equation of a line that passes through $(a,b)$ and is parallel to the vector $(c,d)$.

Group problems

1. Plot the curve $r=3\sin2\theta$ in both the $r\theta$-plane, and the $xy$-plane. [Hint: Make an $(r,\theta)$ table, but pick values for $\theta$ that make $\sin2\theta$ easy to compute. Did you get a clover?]
2. Plot the curve $r=2\theta$ in both the $r\theta$-plane, and the $xy$-plane. [Did you get a spiral?]
   • We know $x=r\cos\theta$ and $y=r\sin\theta$, so for $r=2\theta$ we have $x = 2\theta \cos\theta$ and $y=2\theta\sin\theta$. Find $dx$ and $dy$ in terms of $\theta$ and $d\theta$.
   • Find the slope $\frac{dy}{dx}$ at $\theta = \pi/2$.
3. Let $v=u^2$ and use the coordinates $x=2u+v$, $y=u-2v$.
   • Draw the curve in both the $uv$-plane, and the $xy$-plane (make a $(u,v)$ and $(x,y)$ table).
   • Find $dx$ and $dy$ in terms of $u$ and $du$.
   • Find the slope $dy/dx$ at $u=1$.
   • Give a vector equation of the tangent line to the curve in the $xy$ plane at $u=1$.
4. Let $v=u^3$ and use the coordinates $x=2u+v$, $y=u-2v$.
   • Draw the curve in both the $uv$-plane, and the $xy$-plane (make a $(u,v)$ and $(x,y)$ table).
   • Find $dx$ and $dy$ in terms of $u$ and $du$.
   • Find the slope $dy/dx$ at $u=1$.
   • Give a vector equation of the tangent line to the curve in the $xy$ plane at $u=1$.

Problem Set
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