Polar Graphs Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Describe the graph of r=3r = 3 in polar coordinates.

Solution

  1. 1
    The equation r=3r = 3 means every point is at distance 33 from the origin, regardless of Īø\theta.
  2. 2
    This is the set of all points satisfying x2+y2=9x^2 + y^2 = 9 in rectangular form.
  3. 3
    Therefore, the graph is a circle of radius 33 centered at the origin.

Answer

AĀ circleĀ ofĀ radiusĀ 3Ā centeredĀ atĀ theĀ origin\text{A circle of radius } 3 \text{ centered at the origin}
In polar coordinates, r=cr = c (a constant) always gives a circle centered at the origin with radius āˆ£cāˆ£|c|. This is one of the simplest polar graphs and demonstrates how polar coordinates can express circles very naturally.

About Polar Graphs

Graphs of equations in the form r=f(Īø)r = f(\theta), producing curves such as rose curves, cardioids, limaƧons, and circles in the polar plane.

Learn more about Polar Graphs ā†’

More Polar Graphs Examples

Example 2 medium

Identify the type of polar curve [formula] and find key features.

Example 3 medium

How many petals does the rose curve [formula] have?

Example 4 hard

Find the area enclosed by one petal of the rose curve [formula].

ā† All Polar Graphs Examples Polar Graphs Concept