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Which angle is not coterminal with the other three coterminal angles? -190°, 530°, -450°, 170°

Which angle is not coterminal with the other three coterminal angles? -190°, 530°, -450°, 170°

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.1: Angles
Problem 3E
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**Question:** Which angle is not coterminal with the other three coterminal angles? **Options:** - –190° - 530° - –450° - 170° **Answer Choices:** - A. 530° - B. 170° - C. –450° - D. 190° --- **Explanation:** Coterminal angles are angles that share the same terminal side when drawn in standard position but may have different measures. They can be found by adding or subtracting full rotations (360°) to the given angle. For a thorough analysis of the given angles: 1. **–190°:** - Adding 360° to it: –190° + 360° = 170° 2. **530°:** - Subtracting 360° from it: 530° – 360° = 170° 3. **–450°:** - Adding 360° to it: –450° + 360° = –90° - Adding another 360°: –90° + 360° = 270° 4. **170°:** - This angle is already in standard position and equals 170° By this analysis, angles –190°, 530°, and 170° are coterminal with each other, either directly or through adjustments by full rotations of 360°. However, –450° does not share the same terminal side as the other three. ### Conclusion: - The angle that is **not coterminal** with the other three is **D. –450°**.
Transcribed Image Text:**Question:** Which angle is not coterminal with the other three coterminal angles? **Options:** - –190° - 530° - –450° - 170° **Answer Choices:** - A. 530° - B. 170° - C. –450° - D. 190° --- **Explanation:** Coterminal angles are angles that share the same terminal side when drawn in standard position but may have different measures. They can be found by adding or subtracting full rotations (360°) to the given angle. For a thorough analysis of the given angles: 1. **–190°:** - Adding 360° to it: –190° + 360° = 170° 2. **530°:** - Subtracting 360° from it: 530° – 360° = 170° 3. **–450°:** - Adding 360° to it: –450° + 360° = –90° - Adding another 360°: –90° + 360° = 270° 4. **170°:** - This angle is already in standard position and equals 170° By this analysis, angles –190°, 530°, and 170° are coterminal with each other, either directly or through adjustments by full rotations of 360°. However, –450° does not share the same terminal side as the other three. ### Conclusion: - The angle that is **not coterminal** with the other three is **D. –450°**.
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