Chapter 27: Chapter 27

Problem 846

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What primary angle is coterminal with the angle of $5(1 / 4) \pi$ radians?

Short Answer

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The primary angle coterminal with the angle of $5\frac{1}{4}\pi$ radians is $\frac{-3}{4}\pi$ radians.

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TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Convert the mixed number to an improper fraction

First, we convert the mixed number $5\frac{1}{4}$ to an improper fraction: \[ 5\frac{1}{4} = \frac{21}{4} \] Now, the given angle in radiants can be written as: \[ \frac{21}{4}\pi \]

Step 2: Subtract multiples of $2\pi$

Subtract multiples of $2\pi$ until we get an angle between $0$ and $2\pi$. We notice that $8\pi$ is the largest multiple of $2\pi$ that is less than $\frac{21}{4}\pi$. So, subtract $8\pi$ from our angle: \[ \alpha = \frac{21}{4}\pi - 8\pi = \frac{21}{4}\pi - \frac{32}{4}\pi =\frac{-11}{4}\pi \]

Step 3: Add 2$\pi$ if the result is negative

Since our result is negative, add $2\pi$ to the result to get the coterminal angle within the desired range: \[ \alpha + 2\pi = \frac{-11}{4}\pi + 2\pi = \frac{-11}{4}\pi + \frac{8}{4}\pi = \frac{-3}{4}\pi \] The primary angle coterminal with the angle of $5\frac{1}{4}\pi$ radians is $\frac{-3}{4}\pi$ radians.

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Chapter 27: Chapter 27

What primary angle is coterminal with the angle of \(5(1 / 4) \pi\) radians?

Short Answer

Step by step solution

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Step 1: Convert the mixed number to an improper fraction

Step 2: Subtract multiples of \(2\pi\)

Step 3: Add 2\(\pi\) if the result is negative

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Chapter 3

Chapter 4

Chapter 5

Chapter 6

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Chapter 19

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Chapter 25

Chapter 26

Chapter 28

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Chapter 37

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Chapter 42

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Chapter 46

Chapter 47

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