Polar axis

Definition

The polar axis is the horizontal line in the polar coordinate system from which angles are measured. It usually corresponds to the positive x-axis in Cartesian coordinates.

5 Must Know Facts For Your Next Test

1. Angles in the polar coordinate system are typically measured counterclockwise from the polar axis.
2. The polar axis serves as a reference line for defining polar coordinates $(r, \theta)$ where $\theta$ is the angle from this axis.
3. Positive radius values plot points directly on or above the polar axis, while negative radius values reflect points across it.
4. Equations of lines and curves can be simplified by expressing them relative to their orientation with respect to the polar axis.
5. Symmetry about the polar axis helps simplify graphing and analyzing certain functions.

Review Questions

• What is the role of the polar axis in measuring angles in the polar coordinate system?
• How does reflecting a point across the polar axis affect its coordinates?
• Explain how symmetry about the polar axis can be useful when graphing functions.

Related terms

Polar Coordinates: A coordinate system where each point is determined by a distance from a reference point and an angle from a reference direction.

$r$ (radius): In polar coordinates, $r$ represents the distance from the origin to a point.

$\theta$ (angle): In polar coordinates, $\theta$ represents the angle formed between the positive x-axis (polar axis) and a line connecting the origin to a point.