A circle is represented by the polar equation \(r = 3\cos(\theta)\). What is the center and the radius of this circle?
Answer
Step 3: The center of the circle in polar coordinates is always \((0,0)\) for equations of the form \(r = R\cos(\theta)\) or \(r = R\sin(\theta)\). So, the center of this circle is \((0,0)\).
Step 1 ：Step 1: Recognize the general form of a polar equation of a circle centered at \((0,0)\) which is \(r = R\cos(\theta)\) or \(r = R\sin(\theta)\), where \(R\) is the radius of the circle.
Step 2 ：Step 2: By comparing the given equation \(r = 3\cos(\theta)\) with the general form, we can see that \(R = 3\). Therefore, the radius of the circle is 3.
Step 3 ：Step 3: The center of the circle in polar coordinates is always \((0,0)\) for equations of the form \(r = R\cos(\theta)\) or \(r = R\sin(\theta)\). So, the center of this circle is \((0,0)\).
