Graph r=4cos(x)

Problem

r=4*cos(θ)

Solution

1. Identify the type of polar equation. The equation r=2*a*cos(θ) represents a circle centered on the polar axis (the positive x-axis).

2. Determine the diameter and radius. Comparing r=4*cos(θ) to the standard form, we find 2*a=4 which means the diameter is 4 and the radius is 2

3. Find the center of the circle. In polar coordinates, the center is located at (a,0) which is (2,0) In rectangular coordinates, this is (2,0)

4. Plot key points to verify the shape. At θ=0 r=4*cos(0)=4 At θ=π/3 r=4*cos(π/3)=2 At θ=π/2 r=4*cos(π/2)=0

5. Sketch the graph. The graph is a circle passing through the origin (0,0) with its furthest point at (4,0) on the x-axis, centered at (2,0)

Final Answer

r=4*cos(θ)* is a circle centered at *(2,0)* with radius *2

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