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Active Calculus - Multivariable

Preview Activity 12.5.1.
In this Preview Activity, we will practice converting some equations and regions between rectangular and polar coordinates.
(a)
Draw a plot of each of the curves in the plane described by each of the following polar equations and write a sentence for each graph to explain why the equation is satisfied.
  1. \(\displaystyle r=1\)
  2. \(\displaystyle r=3\)
  3. \(\displaystyle r=0\)
  4. \(\displaystyle \theta =1\)
  5. \(\displaystyle \theta = \frac{3\pi}{4}\)
(b)
Draw a plot of the region given by the following inequalities:
  1. \(\displaystyle 1 \leq r \leq 3\)
  2. \(\displaystyle 1 \leq \theta \leq \frac{3\pi}{4}\)
(c)
Convert the line given by \(y=x\) to polar coordinates and solve your equation in the form \(\theta= \text{constant}\text{.}\)
(d)
Convert the line given by \(x=2\) to polar coordinates and solve your equation in the form \(r= f(\theta)\text{.}\)