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Find all solutions to the equation: sin²(x) + cos(x) = -1. π (A) x = (+2mn) (B) x==²=², 6' (D) (+2mn) (E)x= (+2an) (+2mn) (C) no-

Find all solutions to the equation: sin²(x) + cos(x) = -1. π (A) x = (+2mn) (B) x==²=², 6' (D) (+2mn) (E)x= (+2an) (+2mn) (C) no-

Calculus: Early Transcendentals
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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Title: Solving Trigonometric Equations Text: Find all solutions to the equation: \[ \sin^2(x) + \cos(x) = -1. \] Possible Solution Choices: (A) \( x = \frac{\pi}{6} + 2\pi n \) (B) \( x = -\frac{\pi}{6}, \frac{7\pi}{6} + 2\pi n \) (C) no solutions (D) \( x = \frac{\pi}{2} + 2\pi n \) (E) \( x = -\pi + 2\pi n \) Where \( n \) is any integer. Explanation: In solving this equation, we are dealing with the trigonometric functions sine (\(\sin\)) and cosine (\(\cos\)). The given equation \(\sin^2(x) + \cos(x) = -1\) needs to be explored to find all possible values of \( x \) that satisfy this condition. Each of the provided choices represents a set of possible solutions, but we need to determine which, if any, are correct. Notice that \( n \) stands for any integer, indicating that the solutions are periodic due to the nature of trigonometric functions.
Transcribed Image Text:Title: Solving Trigonometric Equations Text: Find all solutions to the equation: \[ \sin^2(x) + \cos(x) = -1. \] Possible Solution Choices: (A) \( x = \frac{\pi}{6} + 2\pi n \) (B) \( x = -\frac{\pi}{6}, \frac{7\pi}{6} + 2\pi n \) (C) no solutions (D) \( x = \frac{\pi}{2} + 2\pi n \) (E) \( x = -\pi + 2\pi n \) Where \( n \) is any integer. Explanation: In solving this equation, we are dealing with the trigonometric functions sine (\(\sin\)) and cosine (\(\cos\)). The given equation \(\sin^2(x) + \cos(x) = -1\) needs to be explored to find all possible values of \( x \) that satisfy this condition. Each of the provided choices represents a set of possible solutions, but we need to determine which, if any, are correct. Notice that \( n \) stands for any integer, indicating that the solutions are periodic due to the nature of trigonometric functions.
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