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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 9.8.3 .
This activity gives you an opportunity to graph some equations in polar coordinates where
\(r\) is expressed as a function of
\(\theta\text{.}\)
(a) The following activity will take you through how to create a graph of an equation in
\(r\) and
\(\theta\text{.}\)
(i) Draw a graph of
\(y=\cos(x)\) for at least
\(0 \leq x \leq 2 \pi\text{.}\)
(ii) Consider the polar equation
\(r=\cos(\theta)\text{.}\) Complete the table below by computing the value of
\(r\) for each value of
\(\theta\) for this equation.
\(r\) \(\phantom{\displaystyle\frac{\sqrt{2}}{2}}\)
(iii) Plot each of the eleven points you found in the previous part on the polar plane and connect them to make a plot of the graph of
\(r=\cos(\theta)\text{.}\)
(b) Graph the equation
\(r=1+\cos(\theta)\) in the polar plane.
(c) Graph the equation
\(r=1-\cos(\theta)\) in the polar plane.
(d) What are the points of intersections for the graphs of
\(r=1+\cos(\theta)\) and
\(r=1-\cos(\theta)\)
