Final answer:
To sketch the polar equation r = 6, draw a circle centered at the origin with a radius of 6 units, which will be the same in all directions since the radius is constant and does not depend on the angle.
Step-by-step explanation:
To sketch a graph of the polar equation r = 6, we need to understand that this equation represents a circle in polar coordinate system with a fixed radius of 6 units from the origin. Unlike Cartesian coordinates where x and y define a point's location, polar coordinates use a radius and an angle. Here, there is no angle specified, meaning that for any angle θ (theta), the radius r is constant at 6 units. This describes a circle centered at the origin (0,0) with a radius of 6 units on a polar grid.
To visualize this, imagine plotting points on the grid where each point is 6 units away from the center, at various angles ranging from 0 to 360 degrees. As you plot these points and connect them, you will form a circle. The sketch should appear as a perfect circle with no beginning or end, since the radius is the same in all directions.