Rapid Recall

  1. Find the area of a parallelogram whose edges are parallel to the vectors $(1,2)$ and $(3,4)$. (Use the $|ad-bc|$ rule.)
  2. Give a vector equation of a line that passes through the point $(1,2)$ and is parallel to the vector $(3,4)$.
  3. Give a Cartesian equation of a line that passes through the point $(1,2)$ and is parallel to the vector $(3,4)$.

As groups

  1. Draw the polar curve $r=2\cos3\theta$ for $0\leq \theta\leq 2\pi$.
  2. Find the area of a triangle with vertices at $(0,0)$, $(-2,1)$, and $(4,3)$.
  3. Consider the polar curve $r=\frac{2\theta}{\pi}$.
    • Draw the curve (did you get a spiral) for $0\leq \theta\leq 4\pi$.
    • Compute $\frac{dx}{d\theta}$ and $\frac{dy}{d\theta}
    • Set up an integral formula to calculate the length of the curve for $0\leq \theta\leq 2\pi$.
    • Find the slope $dy/dx$ at $\theta=\pi$.
    • Give an equation of the tangent line at $\theta = \pi$.

Problem Set
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