Plot the cardioid given by the polar equation \(r = 1 + cos(\theta)\)
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.
Step 1 ：Step 1: Recognize that the equation is in the form of a cardioid, \(r = a + bcos(\theta)\), 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.
