Polar axis

Definition

The polar axis is the horizontal reference line in the polar coordinate system, analogous to the x-axis in Cartesian coordinates. It is used as a starting point for measuring angles.

5 Must Know Facts For Your Next Test

1. In polar coordinates, angles are measured from the polar axis, usually starting at $0^\circ$ or $0$ radians.
2. The positive direction of the polar axis extends to the right from the pole (origin).
3. The distance from any point to the pole along the polar axis is represented by $r$ when $\theta = 0$.
4. When plotting points and curves in polar coordinates, the angle $\theta$ is measured counterclockwise from the polar axis.
5. The polar axis serves as a line of symmetry for many common polar graphs such as circles and roses.

Review Questions

• What role does the polar axis play in measuring angles in polar coordinates?
• How is distance represented along the polar axis when $\theta = 0$?
• Describe how symmetry with respect to the polar axis might be observed in common polar graphs.

Related terms

Pole: The origin point $(0,0)$ in a polar coordinate system from which distances are measured.

$r$ (radius): The distance from any point in the plane to the pole (origin) in a polar coordinate system.

$\theta$ (angle): The angle measured counterclockwise from the positive direction of the polar axis to a given point's radius vector.