Question

Graph the point with the given polar coordinates, and specify three additional pairs of polar coordinates for the point. $\left(2,120^{\circ}\right)$

   Graph the point with the given polar coordinates, and specify three additional pairs of polar coordinates for the point.
$\left(2,120^{\circ}\right)$

Modern Analytic Geometry

Modern Analytic Geometry

William Wooton,… 1st Edition

Chapter 7, Problem 3

Instant Answer

Step 1

The point \((2, 120^{\circ})\) means that the point is located 2 units away from the origin at an angle of \(120^{\circ}\) measured counterclockwise from the positive x-axis. Step 2: Convert the polar coordinates to Cartesian coordinates to visualize the point. Show more…

Show all steps

lock

Thanks for your feedback!

Graph the point with the given polar coordinates, and specify three additional pairs of polar coordinates for the point. $\left(2,120^{\circ}\right)$

Play audio

Feedback

Powered by NumerAI

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Multiple Representations of a Point in Polar Coordinates

In polar coordinates, a single point can be represented by multiple pairs due to the periodic nature of angles, where adding or subtracting full rotations (360°) yields the same direction. Additionally, a negative radius can be used, which effectively reflects the point across the pole, providing another equivalent representation.

Graphing in Polar Coordinates

Graphing a point given in polar coordinates involves starting at the pole (origin), moving outward the specified distance (radius), and then rotating by the given angle from the polar axis (typically the positive x-axis). This process visually places the point in the correct quadrant of the plane.

Polar Coordinates

The polar coordinate system represents points in the plane using a distance from a reference point (the pole) and an angle measured from a reference direction. This system is an alternative to Cartesian coordinates and is particularly useful in scenarios with circular symmetry.

Recommended Videos

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later