Graph $r=2-2\(\cos\]\theta\)$

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• B.
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Answer: (B)

Verified step by step guidance

1. Recognize that the given polar equation is r = 2 - 2\(\cos\)\(\theta\), which is a limaçon with an inner loop.
2. Identify the general form of a limaçon: r = a - b\(\cos\)\(\theta\). Here, a = 2 and b = 2, which means the limaçon will have an inner loop since a = b.
3. Determine the key points: When \(\theta\) = 0, r = 2 - 2\(\cos\)(0) = 0, indicating the inner loop touches the pole. When \(\theta\) = \(\pi\), r = 2 - 2\(\cos\)(\(\pi\)) = 4, indicating the maximum distance from the pole.
4. Plot the limaçon by starting at the pole (r = 0) when \(\theta\) = 0, then moving outward to the maximum distance (r = 4) at \(\theta\) = \(\pi\), and returning to the pole as \(\theta\) approaches 2\(\pi\).
5. Compare the plotted graph with the provided images to identify the correct graph. The correct graph should show a limaçon with an inner loop, starting and ending at the pole, and reaching a maximum radius of 4.