Plot the point on the polar coordinate system.
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
9. Polar Equations
Polar Coordinate System
Problem 7
Textbook Question
Indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (3, −135°)

Verified step by step guidance1
Recall that polar coordinates are given in the form \((r, \theta)\), where \(r\) is the distance from the origin and \(\theta\) is the angle measured counterclockwise from the positive x-axis.
Note that the given point is \((3, -135^\circ)\). Since the angle is negative, convert it to a positive angle by adding \(360^\circ\): \(-135^\circ + 360^\circ = 225^\circ\).
Plot the point by moving a distance of 3 units from the origin in the direction of \(225^\circ\). This angle lies in the third quadrant of the Cartesian plane.
Identify which labeled point (A, B, C, or D) on the graph corresponds to the location at \$3$ units from the origin along the \(225^\circ\) direction.
Confirm your choice by checking the position of the point relative to the axes and the given labels on the graph.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
0 Comments
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polar Coordinates System
Polar coordinates represent points in a plane using a distance from the origin (radius) and an angle measured from the positive x-axis. Each point is given as (r, θ), where r is the radius and θ is the angle in degrees or radians.
Recommended video:
Intro to Polar Coordinates
Negative Angles in Polar Coordinates
A negative angle in polar coordinates means measuring the angle clockwise from the positive x-axis. For example, −135° is equivalent to rotating 135° clockwise, which can be converted to a positive angle by adding 360°, resulting in 225°.
Recommended video:
Intro to Polar Coordinates
Plotting Points with Negative Radius
If the radius r is positive, the point lies in the direction of the angle θ. If r is negative, the point is plotted in the opposite direction of θ by rotating 180°. In this question, r is positive, so the point lies 3 units from the origin at the angle −135°.
Recommended video:
Graphing Two Variable Equations by Plotting Points
Related Videos
Related Practice
Multiple Choice
972
views
