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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.
\(\displaystyle r=1\)
\(\displaystyle r=3\)
\(\displaystyle r=0\)
\(\displaystyle \theta =1\)
\(\displaystyle \theta = \frac{3\pi}{4}\)
(b)
Draw a plot of the region given by the following inequalities:
\(\displaystyle 1 \leq r \leq 3\)
\(\displaystyle 1 \leq \theta \leq \frac{3\pi}{4}\)
(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
\(r= f(\theta)\text{.}\)