Polar grid

Definition

A polar grid is a coordinate system where points are determined by a distance from a reference point (the pole) and an angle from a reference direction. It is often used for problems involving symmetry and circular shapes.

5 Must Know Facts For Your Next Test

1. Polar coordinates are given as $(r, \theta)$, where $r$ represents the radius (distance from the pole) and $\theta$ is the angle measured in radians or degrees.
2. The polar grid consists of concentric circles centered at the pole and rays emanating from the pole at regular angular intervals.
3. Conversion between polar and Cartesian coordinates involves $x = r \cos(\theta)$ and $y = r \sin(\theta)$ for converting to Cartesian, and $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}(\frac{y}{x})$ for converting to polar.
4. Polar equations can represent curves such as circles, spirals, and roses that are more complex to describe using Cartesian coordinates.
5. The angle $\theta$ in polar coordinates can be positive or negative; positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise.

Review Questions

• What are the formulas for converting between polar and Cartesian coordinates?
• How would you plot the point $(3, \frac{\pi}{4})$ on a polar grid?
• What type of graph does the polar equation $r = 2 + 3 \cos(\theta)$ represent?

Related terms

Polar Coordinates: A coordinate system where each point on a plane is defined by its distance from a reference point (the pole) and an angle from a reference direction.

Cartesian Coordinates: A coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates which are distances to two fixed perpendicular directed lines, measured in the same unit of length.

Radius: In polar coordinates, it represents the distance from the pole (origin) to a specific point.