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Which angle is NOT coterminal with 5л radians? 4

Which angle is NOT coterminal with 5л radians? 4

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.2: Angles And Their Relationships
Problem 37E: Draw a triangle with three acute angles. Construct angle bisectors for each of the three angles. On...
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### Question **Which angle is NOT coterminal with \(\frac{5\pi}{4}\) radians?** ### Answer Choices **A)** \(\frac{-3\pi}{4}\) **B)** \(\frac{7\pi}{4}\) **C)** \(\frac{-11\pi}{4}\) **D)** \(\frac{13\pi}{4}\) ### Answer Selection - \( \circ \) a \(A\) - \( \circ \) b \(B\) - \( \circ \) c \(C\) - \( \circ \) d \(D\) ### Explanation To determine which angles are coterminal with \(\frac{5\pi}{4}\) radians, we need to understand that coterminal angles differ by full rotations (multiples of \(2\pi\)). Given the choices, we need to check each angle to see if it aligns with \(\frac{5\pi}{4}\) when a multiple of \(2\pi\) is added or subtracted: 1. **Choice A: \(\frac{-3\pi}{4}\)** - Adding \( \frac{8\pi}{4} \) (which is \(2\pi\)) to \(\frac{-3\pi}{4}\): - \(\frac{-3\pi}{4} + \frac{8\pi}{4} = \frac{5\pi}{4}\) - Therefore, \(\frac{-3\pi}{4}\) is coterminal with \(\frac{5\pi}{4}\). 2. **Choice B: \(\frac{7\pi}{4}\)** - Adding \( \frac{-8\pi}{4} \) (which is \(-2\pi\)) to \(\frac{7\pi}{4}\): - \(\frac{7\pi}{4} - \frac{8\pi}{4} = \frac{-\pi}{4}\) - When looking to see if \(\frac{-\pi}{4}\) can become \(\frac{5\pi}{4}\) by adding or subtracting \(2\pi\): - \(\frac{-\pi}{4} + \frac{8\pi}{4} = \frac
Transcribed Image Text:### Question **Which angle is NOT coterminal with \(\frac{5\pi}{4}\) radians?** ### Answer Choices **A)** \(\frac{-3\pi}{4}\) **B)** \(\frac{7\pi}{4}\) **C)** \(\frac{-11\pi}{4}\) **D)** \(\frac{13\pi}{4}\) ### Answer Selection - \( \circ \) a \(A\) - \( \circ \) b \(B\) - \( \circ \) c \(C\) - \( \circ \) d \(D\) ### Explanation To determine which angles are coterminal with \(\frac{5\pi}{4}\) radians, we need to understand that coterminal angles differ by full rotations (multiples of \(2\pi\)). Given the choices, we need to check each angle to see if it aligns with \(\frac{5\pi}{4}\) when a multiple of \(2\pi\) is added or subtracted: 1. **Choice A: \(\frac{-3\pi}{4}\)** - Adding \( \frac{8\pi}{4} \) (which is \(2\pi\)) to \(\frac{-3\pi}{4}\): - \(\frac{-3\pi}{4} + \frac{8\pi}{4} = \frac{5\pi}{4}\) - Therefore, \(\frac{-3\pi}{4}\) is coterminal with \(\frac{5\pi}{4}\). 2. **Choice B: \(\frac{7\pi}{4}\)** - Adding \( \frac{-8\pi}{4} \) (which is \(-2\pi\)) to \(\frac{7\pi}{4}\): - \(\frac{7\pi}{4} - \frac{8\pi}{4} = \frac{-\pi}{4}\) - When looking to see if \(\frac{-\pi}{4}\) can become \(\frac{5\pi}{4}\) by adding or subtracting \(2\pi\): - \(\frac{-\pi}{4} + \frac{8\pi}{4} = \frac
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