Which angle is not coterminal with the other three coterminal angles? 135°, 855°, -155°, -225° A.-225° C. 855° B. 135° D. -155°

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter8: Applications Of Trigonometry
Section: Chapter Questions
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### Understanding Coterminal Angles

#### Question:
Which angle is not coterminal with the other three coterminal angles?

- 135°
- 855°
- -155°
- -225°

#### Options:
- A: -225°
- B: 135°
- C: 855°
- D: -155°

#### Explanation:
Coterminal angles are angles that share the same initial and terminal sides when drawn in standard position. To determine if the given angles are coterminal, we can add or subtract multiples of 360° (since a full rotation is 360°).

1. **135°:**
   - It's the primary angle.

2. **855°:**
   - 855° can be simplified by subtracting 360° until it's between 0° and 360°.
   - 855° - 360° = 495°
   - 495° - 360° = 135°
   - 855° is coterminal with 135°.

3. **-155°:**
   - -155° can be simplified by adding 360°.
   - -155° + 360° = 205°
   - 205° is not coterminal with 135°.

4. **-225°:**
   - -225° can be simplified by adding 360°.
   - -225° + 360° = 135°
   - -225° is coterminal with 135°.

#### Conclusion:
Reviewing the above calculations, the angle -155° is not coterminal with the other three angles.

**Correct Answer: D: -155°**

---

This example illustrates how to determine whether angles are coterminal using simple arithmetic operations. For any educational content that involves trigonometry, it is essential to understand the concept of coterminal angles, as they play a significant role in angle measurements and periodic functions.
Transcribed Image Text:### Understanding Coterminal Angles #### Question: Which angle is not coterminal with the other three coterminal angles? - 135° - 855° - -155° - -225° #### Options: - A: -225° - B: 135° - C: 855° - D: -155° #### Explanation: Coterminal angles are angles that share the same initial and terminal sides when drawn in standard position. To determine if the given angles are coterminal, we can add or subtract multiples of 360° (since a full rotation is 360°). 1. **135°:** - It's the primary angle. 2. **855°:** - 855° can be simplified by subtracting 360° until it's between 0° and 360°. - 855° - 360° = 495° - 495° - 360° = 135° - 855° is coterminal with 135°. 3. **-155°:** - -155° can be simplified by adding 360°. - -155° + 360° = 205° - 205° is not coterminal with 135°. 4. **-225°:** - -225° can be simplified by adding 360°. - -225° + 360° = 135° - -225° is coterminal with 135°. #### Conclusion: Reviewing the above calculations, the angle -155° is not coterminal with the other three angles. **Correct Answer: D: -155°** --- This example illustrates how to determine whether angles are coterminal using simple arithmetic operations. For any educational content that involves trigonometry, it is essential to understand the concept of coterminal angles, as they play a significant role in angle measurements and periodic functions.
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