### Matching Points in Polar Coordinates This educational exercise involves matching a given point in polar coordinates to the correct point on a Cartesian graph. The problem provides the polar coordinates: \[ \left( -2, \frac{5\pi}{6} \right) \] ### Instruction: Match the point in polar coordinates with either A, B, C, or D on the graph. ### Graph Description: The graph is a Cartesian coordinate system with both the x-axis and y-axis clearly marked with positive and negative values. The axes are labeled as follows: - The x-axis ranges from -3 to 3. - The y-axis ranges from -3 to 3. ### Labeled Points on Graph: - **Point A** is located at Cartesian coordinates (3, 0). - **Point B** is located at Cartesian coordinates (0, 3). - **Point C** is located at Cartesian coordinates (-3, 0). - **Point D** is located at Cartesian coordinates (0, -3). ### Objective: Using the given polar coordinates \(\left( -2, \frac{5\pi}{6} \right)\), identify the corresponding point (A, B, C, or D) on the Cartesian coordinate system. To convert polar coordinates to Cartesian coordinates: \[ x = r \cos(\theta) \] \[ y = r \sin(\theta) \] #### Step-by-Step Conversion: 1. \( r = -2 \) 2. \( \theta = \frac{5\pi}{6} \) Calculate \( x \) and \( y \): \[ x = -2 \cos\left(\frac{5\pi}{6}\right) \] \[ y = -2 \sin\left(\frac{5\pi}{6}\right) \] Hence, by determining x and y values from the conversion, you can match the Cartesian coordinates to one of the labeled points A, B, C, or D on the graph.
### Matching Points in Polar Coordinates This educational exercise involves matching a given point in polar coordinates to the correct point on a Cartesian graph. The problem provides the polar coordinates: \[ \left( -2, \frac{5\pi}{6} \right) \] ### Instruction: Match the point in polar coordinates with either A, B, C, or D on the graph. ### Graph Description: The graph is a Cartesian coordinate system with both the x-axis and y-axis clearly marked with positive and negative values. The axes are labeled as follows: - The x-axis ranges from -3 to 3. - The y-axis ranges from -3 to 3. ### Labeled Points on Graph: - **Point A** is located at Cartesian coordinates (3, 0). - **Point B** is located at Cartesian coordinates (0, 3). - **Point C** is located at Cartesian coordinates (-3, 0). - **Point D** is located at Cartesian coordinates (0, -3). ### Objective: Using the given polar coordinates \(\left( -2, \frac{5\pi}{6} \right)\), identify the corresponding point (A, B, C, or D) on the Cartesian coordinate system. To convert polar coordinates to Cartesian coordinates: \[ x = r \cos(\theta) \] \[ y = r \sin(\theta) \] #### Step-by-Step Conversion: 1. \( r = -2 \) 2. \( \theta = \frac{5\pi}{6} \) Calculate \( x \) and \( y \): \[ x = -2 \cos\left(\frac{5\pi}{6}\right) \] \[ y = -2 \sin\left(\frac{5\pi}{6}\right) \] Hence, by determining x and y values from the conversion, you can match the Cartesian coordinates to one of the labeled points A, B, C, or D on the graph.
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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![### Matching Points in Polar Coordinates
This educational exercise involves matching a given point in polar coordinates to the correct point on a Cartesian graph.
The problem provides the polar coordinates:
\[ \left( -2, \frac{5\pi}{6} \right) \]
### Instruction:
Match the point in polar coordinates with either A, B, C, or D on the graph.
### Graph Description:
The graph is a Cartesian coordinate system with both the x-axis and y-axis clearly marked with positive and negative values. The axes are labeled as follows:
- The x-axis ranges from -3 to 3.
- The y-axis ranges from -3 to 3.
### Labeled Points on Graph:
- **Point A** is located at Cartesian coordinates (3, 0).
- **Point B** is located at Cartesian coordinates (0, 3).
- **Point C** is located at Cartesian coordinates (-3, 0).
- **Point D** is located at Cartesian coordinates (0, -3).
### Objective:
Using the given polar coordinates \(\left( -2, \frac{5\pi}{6} \right)\), identify the corresponding point (A, B, C, or D) on the Cartesian coordinate system.
To convert polar coordinates to Cartesian coordinates:
\[ x = r \cos(\theta) \]
\[ y = r \sin(\theta) \]
#### Step-by-Step Conversion:
1. \( r = -2 \)
2. \( \theta = \frac{5\pi}{6} \)
Calculate \( x \) and \( y \):
\[ x = -2 \cos\left(\frac{5\pi}{6}\right) \]
\[ y = -2 \sin\left(\frac{5\pi}{6}\right) \]
Hence, by determining x and y values from the conversion, you can match the Cartesian coordinates to one of the labeled points A, B, C, or D on the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65a51a67-e1b7-4efc-8ebc-3bc066e5507a%2Fd739ebba-36fb-4abe-b062-bee7d1e0caae%2Fo0pnln9.jpeg&w=3840&q=75)
Transcribed Image Text:### Matching Points in Polar Coordinates
This educational exercise involves matching a given point in polar coordinates to the correct point on a Cartesian graph.
The problem provides the polar coordinates:
\[ \left( -2, \frac{5\pi}{6} \right) \]
### Instruction:
Match the point in polar coordinates with either A, B, C, or D on the graph.
### Graph Description:
The graph is a Cartesian coordinate system with both the x-axis and y-axis clearly marked with positive and negative values. The axes are labeled as follows:
- The x-axis ranges from -3 to 3.
- The y-axis ranges from -3 to 3.
### Labeled Points on Graph:
- **Point A** is located at Cartesian coordinates (3, 0).
- **Point B** is located at Cartesian coordinates (0, 3).
- **Point C** is located at Cartesian coordinates (-3, 0).
- **Point D** is located at Cartesian coordinates (0, -3).
### Objective:
Using the given polar coordinates \(\left( -2, \frac{5\pi}{6} \right)\), identify the corresponding point (A, B, C, or D) on the Cartesian coordinate system.
To convert polar coordinates to Cartesian coordinates:
\[ x = r \cos(\theta) \]
\[ y = r \sin(\theta) \]
#### Step-by-Step Conversion:
1. \( r = -2 \)
2. \( \theta = \frac{5\pi}{6} \)
Calculate \( x \) and \( y \):
\[ x = -2 \cos\left(\frac{5\pi}{6}\right) \]
\[ y = -2 \sin\left(\frac{5\pi}{6}\right) \]
Hence, by determining x and y values from the conversion, you can match the Cartesian coordinates to one of the labeled points A, B, C, or D on the graph.
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