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Which angle is not coterminal with the other three coterminal angles? -145°, 625°, -865°, 215°

Which angle is not coterminal with the other three coterminal angles? -145°, 625°, -865°, 215°

Trigonometry (11th Edition)
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°.
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**Educational Exercise: Identifying Coterminal Angles** **Question:** Which angle is not coterminal with the other three coterminal angles? **Options:** - A. 625° - B. -145° - C. -865° - D. 215° **Explanation:** Coterminal angles are angles that share the same initial side and terminal side but may have different rotations. To check if angles are coterminal, you can add or subtract integer multiples of 360°. **Solution Steps:** 1. **Convert each angle to its equivalent angle within 0° to 360° range:** - \( 625°: 625° - 360° = 265° \) - \( -145°: -145° + 360° = 215° \) - \( -865°: -865° + 2(360°) = -865° + 720° = -145° \) - \( 215° \) is already within the 0° to 360° range. 2. **Check which angles are coterminal:** - 625° and -865° reduce to 265° and -145° respectively, which appear distinct but similar under modulo operations. - -145° and 215° share the same angle equivalence of 215°. - Due to this resultant deviation, 265° derived from 625° is the odd one out. **Answer:** - **A. 625°** is not coterminal with the other three angles. This problem enhances understanding of angle equivalence under rotations and coterminality concepts. *2023 International Academy of Science. All Rights Reserved.*
Transcribed Image Text:**Educational Exercise: Identifying Coterminal Angles** **Question:** Which angle is not coterminal with the other three coterminal angles? **Options:** - A. 625° - B. -145° - C. -865° - D. 215° **Explanation:** Coterminal angles are angles that share the same initial side and terminal side but may have different rotations. To check if angles are coterminal, you can add or subtract integer multiples of 360°. **Solution Steps:** 1. **Convert each angle to its equivalent angle within 0° to 360° range:** - \( 625°: 625° - 360° = 265° \) - \( -145°: -145° + 360° = 215° \) - \( -865°: -865° + 2(360°) = -865° + 720° = -145° \) - \( 215° \) is already within the 0° to 360° range. 2. **Check which angles are coterminal:** - 625° and -865° reduce to 265° and -145° respectively, which appear distinct but similar under modulo operations. - -145° and 215° share the same angle equivalence of 215°. - Due to this resultant deviation, 265° derived from 625° is the odd one out. **Answer:** - **A. 625°** is not coterminal with the other three angles. This problem enhances understanding of angle equivalence under rotations and coterminality concepts. *2023 International Academy of Science. All Rights Reserved.*
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