Plot the point given in polar coordinates. 5,- Select the graph that represents the point -5,- OA. 1. OB. O C. Ay O D. # Q Q 5
Plot the point given in polar coordinates. 5,- Select the graph that represents the point -5,- OA. 1. OB. O C. Ay O D. # Q Q 5
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Plot the point given in polar coordinates.
\[
\left( -5, -\frac{\pi}{3} \right)
\]
### Select the graph that represents the point \(\left( -5, -\frac{\pi}{3} \right)\).
**Options:**
#### A
- A graph with the point plotted in the third quadrant. The angle is drawn negatively, and the radius extends in the opposite direction to place the point in the correct position.
#### B
- A graph where the angle and the radius point suggest incorrect quadrant placement.
#### C
- A graph with the point plotted incorrectly in the first quadrant.
#### D
- The point is plotted in the third quadrant, consistent with a negative radius and angle.
### Explanation:
- **Polar Coordinates:** In polar coordinates, a point is represented by \( (r, \theta) \), where \( r \) is the radius (distance from the origin) and \( \theta \) is the angle from the positive x-axis.
- **Negative Radius:** A negative radius means the direction is reversed. The angle \( -\frac{\pi}{3} \) indicates a clockwise rotation equivalent to \( \frac{4\pi}{3} \).
To correctly plot the point \( \left( -5, -\frac{\pi}{3} \right) \):
1. Rotate \( \frac{\pi}{3} \) clockwise.
2. Extend the radius in the opposite direction due to the negative value.
3. The point should lie in the third quadrant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ef72b86-64c9-44dd-905e-4169b5b508ab%2F7ca0a2df-6577-4e02-96ad-23645219ba9f%2Ffac0nes_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Plot the point given in polar coordinates.
\[
\left( -5, -\frac{\pi}{3} \right)
\]
### Select the graph that represents the point \(\left( -5, -\frac{\pi}{3} \right)\).
**Options:**
#### A
- A graph with the point plotted in the third quadrant. The angle is drawn negatively, and the radius extends in the opposite direction to place the point in the correct position.
#### B
- A graph where the angle and the radius point suggest incorrect quadrant placement.
#### C
- A graph with the point plotted incorrectly in the first quadrant.
#### D
- The point is plotted in the third quadrant, consistent with a negative radius and angle.
### Explanation:
- **Polar Coordinates:** In polar coordinates, a point is represented by \( (r, \theta) \), where \( r \) is the radius (distance from the origin) and \( \theta \) is the angle from the positive x-axis.
- **Negative Radius:** A negative radius means the direction is reversed. The angle \( -\frac{\pi}{3} \) indicates a clockwise rotation equivalent to \( \frac{4\pi}{3} \).
To correctly plot the point \( \left( -5, -\frac{\pi}{3} \right) \):
1. Rotate \( \frac{\pi}{3} \) clockwise.
2. Extend the radius in the opposite direction due to the negative value.
3. The point should lie in the third quadrant.
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