Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Question:**
Plot the point that has the given polar coordinates:
\[
\left( 5, -\frac{2\pi}{3} \right)
\]
**Description of Graphs:**
There are four polar coordinate grids arranged in a 2x2 layout. Each grid is a circle centered at the origin, with concentric circles representing different radial distances and lines representing angles. The radial distances are labeled from -6 to 6. The angles are marked on the graphs in radians with some labeled lines at \(0\), \(\frac{\pi}{2}\), \(\pi\), and \(\frac{3\pi}{2}\).
Each grid contains one plotted point, but only one grid will have the point that correctly corresponds to the given polar coordinates.
1. **Top Left Grid:**
- A point is plotted at a radius of approximately 5 and an angle of \(-\frac{2\pi}{3}\).
2. **Top Right Grid:**
- A point is plotted at some other coordinates unrelated to \(-\frac{2\pi}{3}\).
3. **Bottom Left Grid:**
- A point is plotted at some other coordinates unrelated to \(-\frac{2\pi}{3}\).
4. **Bottom Right Grid:**
- A point is plotted at some other coordinates unrelated to \(-\frac{2\pi}{3}\).
**Guidance:**
Identify the grid where \(\left( 5, -\frac{2\pi}{3} \right)\) is accurately plotted. In polar coordinates, the first value indicates the radial distance from the origin, while the second value indicates the angle in radians from the positive x-axis.
The correct plot would be where these conditions meet, specifically on the top left grid. Upon verification, ensure the radial length is 5 and the angle is measured clockwise from the positive x-axis by \(\frac{2\pi}{3}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d796b34-b07f-46f8-a383-20e8200b843a%2F56aab558-45cb-4b77-83c5-af874db9935c%2Fl6ozfcs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Plot the point that has the given polar coordinates:
\[
\left( 5, -\frac{2\pi}{3} \right)
\]
**Description of Graphs:**
There are four polar coordinate grids arranged in a 2x2 layout. Each grid is a circle centered at the origin, with concentric circles representing different radial distances and lines representing angles. The radial distances are labeled from -6 to 6. The angles are marked on the graphs in radians with some labeled lines at \(0\), \(\frac{\pi}{2}\), \(\pi\), and \(\frac{3\pi}{2}\).
Each grid contains one plotted point, but only one grid will have the point that correctly corresponds to the given polar coordinates.
1. **Top Left Grid:**
- A point is plotted at a radius of approximately 5 and an angle of \(-\frac{2\pi}{3}\).
2. **Top Right Grid:**
- A point is plotted at some other coordinates unrelated to \(-\frac{2\pi}{3}\).
3. **Bottom Left Grid:**
- A point is plotted at some other coordinates unrelated to \(-\frac{2\pi}{3}\).
4. **Bottom Right Grid:**
- A point is plotted at some other coordinates unrelated to \(-\frac{2\pi}{3}\).
**Guidance:**
Identify the grid where \(\left( 5, -\frac{2\pi}{3} \right)\) is accurately plotted. In polar coordinates, the first value indicates the radial distance from the origin, while the second value indicates the angle in radians from the positive x-axis.
The correct plot would be where these conditions meet, specifically on the top left grid. Upon verification, ensure the radial length is 5 and the angle is measured clockwise from the positive x-axis by \(\frac{2\pi}{3}\).
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