Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![## Problem 14: Trigonometric Equation
### Objective:
Solve the equation for the principal values of \( x \).
### Equation:
\[ 2 \cos^2 x - 5 \cos x + 2 = 0 \]
### Options:
- **A:** \( 0^\circ \) and \( 30^\circ \)
- **B:** \( 30^\circ \)
- **C:** \( 60^\circ \)
- **D:** \( 60^\circ \) and \( 300^\circ \)
The correct answer is circled: **C: 60°**.
### Explanation:
To solve this equation, you can use trigonometric identities or factorization techniques to find the values of \( x \) that satisfy the equation within the principal range \([0^\circ, 360^\circ)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb805b29b-1703-42be-83a9-c544ba7b8f1b%2F0dec9990-850f-4303-b05e-5eb7164082ca%2Fzkvnylo_processed.png&w=3840&q=75)
Transcribed Image Text:## Problem 14: Trigonometric Equation
### Objective:
Solve the equation for the principal values of \( x \).
### Equation:
\[ 2 \cos^2 x - 5 \cos x + 2 = 0 \]
### Options:
- **A:** \( 0^\circ \) and \( 30^\circ \)
- **B:** \( 30^\circ \)
- **C:** \( 60^\circ \)
- **D:** \( 60^\circ \) and \( 300^\circ \)
The correct answer is circled: **C: 60°**.
### Explanation:
To solve this equation, you can use trigonometric identities or factorization techniques to find the values of \( x \) that satisfy the equation within the principal range \([0^\circ, 360^\circ)\).
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