Give two sets of polar coordinates for each of the points A-F in the figure. E C IN LA Im JU 4 5-6 1 2 3 4 5 Give two sets of polar coordinates for point A. Select all that apply. A. C. E. A. C. E. A. R|M C. (-4.4 Give two sets of polar coordinates for point B. Select all that apply. 5. 5T 5T 6 5 R|N 7μ B. (4,0) Зл (-2,-327 D. (-4,1) F. E. (-2,0) B. D. F. Give two sets of polar coordinates for point C. Select all that apply. B. Зл (5-7) 5. F. เก N TU 11x (5.1) 6 D. (4) (2) 3 41 5π

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Educational Website Content: Polar Coordinates Exercise**

### Polar Coordinate System

The figure on the left illustrates a set of polar coordinates, with points A, B, C, D, E, and F plotted on the polar grid. The polar grid is composed of circles with a common center at the origin and lines radiating from the center at various angles (θ) measured in radians. The radial lines are marked with angles like π/6, π/4, π/3, indicating how the angle θ increases counterclockwise from the polar axis.

### Task

Your task is to identify two sets of polar coordinates for each of the points A-F labeled in the figure. For each point, multiple-choice options are provided to select the possible polar coordinates. 

### Directions

1. **Identify Two Sets of Polar Coordinates for Point A:**

   - Options Available:
     - A. \( \left(-4, \frac{5\pi}{4}\right) \)
     - B. \( (4, 0) \)
     - C. \( \left(4, \frac{\pi}{3}\right) \)
     - D. \( (-4, \pi) \)
     - E. \( \left(-4, \frac{4\pi}{3}\right) \)
     - F. \( \left(4, \frac{3\pi}{4}\right) \)

2. **Identify Two Sets of Polar Coordinates for Point B:**

   - Options Available:
     - A. \( \left(5, \frac{\pi}{6}\right) \)
     - B. \( \left(5, \frac{\pi}{6}\right) \)
     - C. \( \left(5, \frac{\pi}{2}\right) \)
     - D. \( \left(-5, \frac{\pi}{3}\right) \)
     - E. \( \left(-5, \frac{7\pi}{6}\right) \)
     - F. \( \left(5, \frac{11\pi}{6}\right) \)

3. **Identify Two Sets of Polar Coordinates for Point C:**

   - Options Available:
     - A. \( \left(-2, \frac{3\pi}{2}\right) \)
     - B. \( \left(2, \frac{4\pi}{3
Transcribed Image Text:**Educational Website Content: Polar Coordinates Exercise** ### Polar Coordinate System The figure on the left illustrates a set of polar coordinates, with points A, B, C, D, E, and F plotted on the polar grid. The polar grid is composed of circles with a common center at the origin and lines radiating from the center at various angles (θ) measured in radians. The radial lines are marked with angles like π/6, π/4, π/3, indicating how the angle θ increases counterclockwise from the polar axis. ### Task Your task is to identify two sets of polar coordinates for each of the points A-F labeled in the figure. For each point, multiple-choice options are provided to select the possible polar coordinates. ### Directions 1. **Identify Two Sets of Polar Coordinates for Point A:** - Options Available: - A. \( \left(-4, \frac{5\pi}{4}\right) \) - B. \( (4, 0) \) - C. \( \left(4, \frac{\pi}{3}\right) \) - D. \( (-4, \pi) \) - E. \( \left(-4, \frac{4\pi}{3}\right) \) - F. \( \left(4, \frac{3\pi}{4}\right) \) 2. **Identify Two Sets of Polar Coordinates for Point B:** - Options Available: - A. \( \left(5, \frac{\pi}{6}\right) \) - B. \( \left(5, \frac{\pi}{6}\right) \) - C. \( \left(5, \frac{\pi}{2}\right) \) - D. \( \left(-5, \frac{\pi}{3}\right) \) - E. \( \left(-5, \frac{7\pi}{6}\right) \) - F. \( \left(5, \frac{11\pi}{6}\right) \) 3. **Identify Two Sets of Polar Coordinates for Point C:** - Options Available: - A. \( \left(-2, \frac{3\pi}{2}\right) \) - B. \( \left(2, \frac{4\pi}{3
**Polar Coordinates Selection Exercise**

### Instructions:

For each point (D, E, F), identify two sets of polar coordinates. Check all options that apply.

---

#### Point D: Select all that apply.

- A. \(\left(-3, -\frac{3\pi}{2}\right)\)
- B. \(\left(-3, \frac{4\pi}{3}\right)\)
- C. \((-3, 0)\)
- D. \(\left(3, \frac{\pi}{2}\right)\)
- E. \((3, \pi)\)
- F. \(\left(3, \frac{\pi}{6}\right)\)

---

#### Point E: Select all that apply.

- A. \(\left(4, \frac{5\pi}{4}\right)\)
- B. \(\left(-4, \frac{3\pi}{2}\right)\)
- C. \(\left(-4, \frac{7\pi}{6}\right)\)
- D. \(\left(4, \frac{\pi}{4}\right)\)
- E. \(\left(4, \frac{3\pi}{4}\right)\)
- F. \(\left(4, \frac{11\pi}{6}\right)\)

---

#### Point F: Select all that apply.

- A. \(\left(-4, \frac{2\pi}{3}\right)\)
- B. \(\left(4, \frac{\pi}{6}\right)\)
- C. \(\left(4, \frac{5\pi}{3}\right)\)
- D. \(\left(-4, \frac{\pi}{6}\right)\)
- E. \(\left(-4, \frac{7\pi}{6}\right)\)
- F. \(\left(4, \frac{4\pi}{3}\right)\)

---

Make sure to consider both the radius and the angle when selecting the correct polar coordinates for each point.
Transcribed Image Text:**Polar Coordinates Selection Exercise** ### Instructions: For each point (D, E, F), identify two sets of polar coordinates. Check all options that apply. --- #### Point D: Select all that apply. - A. \(\left(-3, -\frac{3\pi}{2}\right)\) - B. \(\left(-3, \frac{4\pi}{3}\right)\) - C. \((-3, 0)\) - D. \(\left(3, \frac{\pi}{2}\right)\) - E. \((3, \pi)\) - F. \(\left(3, \frac{\pi}{6}\right)\) --- #### Point E: Select all that apply. - A. \(\left(4, \frac{5\pi}{4}\right)\) - B. \(\left(-4, \frac{3\pi}{2}\right)\) - C. \(\left(-4, \frac{7\pi}{6}\right)\) - D. \(\left(4, \frac{\pi}{4}\right)\) - E. \(\left(4, \frac{3\pi}{4}\right)\) - F. \(\left(4, \frac{11\pi}{6}\right)\) --- #### Point F: Select all that apply. - A. \(\left(-4, \frac{2\pi}{3}\right)\) - B. \(\left(4, \frac{\pi}{6}\right)\) - C. \(\left(4, \frac{5\pi}{3}\right)\) - D. \(\left(-4, \frac{\pi}{6}\right)\) - E. \(\left(-4, \frac{7\pi}{6}\right)\) - F. \(\left(4, \frac{4\pi}{3}\right)\) --- Make sure to consider both the radius and the angle when selecting the correct polar coordinates for each point.
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