Problem

Identify and graph the limaçon described by the polar equation r=1+2cos⁡θ.

Answer

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Answer

Step 3: Graph the limaçon. Plot points for various angles and connect the points smoothly, making sure to include the inner loop.

Steps

Step 1 ：Step 1: Identify the type of limaçon. Here, the equation is of the form r=a+bcos⁡θ or r=a+bsin⁡θ where a = 1 and b = 2. Because b > a, this is a limaçon with an inner loop.

Step 2 ：Step 2: Identify the characteristics of the limaçon. The limaçon makes a loop inside the circle r=1 and crosses the pole at r=1+2=3 when cos⁡θ=1 and at r=1−2=−1 when cos⁡θ=−1.

Step 3 ：Step 3: Graph the limaçon. Plot points for various angles and connect the points smoothly, making sure to include the inner loop.

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