Problem

Plot the cardioid given by the polar equation r=1+cos(θ)

Answer

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Answer

Step 4: Plot the cardioid. Start at the pole (the origin). The cardioid starts at the point r=2 (the size) on the right of the pole (since it's oriented to the right). The cardioid loops around the pole and comes back to the starting point, creating a heart shape.

Steps

Step 1 ：Step 1: Recognize that the equation is in the form of a cardioid, r=a+bcos(θ), where a=1 and b=1.

Step 2 ：Step 2: Identify the orientation of the cardioid. Since b>0, the cardioid is oriented to the right.

Step 3 ：Step 3: Identify the size of the cardioid. The size of the cardioid is determined by the sum a+|b|=1+1=2.

Step 4 ：Step 4: Plot the cardioid. Start at the pole (the origin). The cardioid starts at the point r=2 (the size) on the right of the pole (since it's oriented to the right). The cardioid loops around the pole and comes back to the starting point, creating a heart shape.

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