Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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**Title: Solving Trigonometric Equations** **Introduction:** In this segment, we explore solving the given trigonometric equation. **Problem Statement:** Find the solution set of \[7 \sin(\theta) = 5 \sin(\theta)\] **Solution Process:** To find the solution set, follow these steps: 1. **Subtract \(5 \sin(\theta)\) from both sides:** \[ 7 \sin(\theta) - 5 \sin(\theta) = 0 \] 2. **Combine like terms:** \[ 2 \sin(\theta) = 0 \] 3. **Divide by 2:** \[ \sin(\theta) = 0 \] The solutions to \(\sin(\theta) = 0\) are the angles where the sine function equals zero. These angles occur at: \[ \theta = n\pi \quad \text{for integer } n \] **Conclusion:** The solution set for the given trigonometric equation \(7 \sin(\theta) = 5 \sin(\theta)\) is: \[ \boxed{\theta = n\pi \text{ for integer } n} \] Understanding how to manipulate and solve basic trigonometric equations is essential in mathematics and can be applied to various fields including physics, engineering, and computer science.
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Transcribed Image Text:**Title: Solving Trigonometric Equations** **Introduction:** In this segment, we explore solving the given trigonometric equation. **Problem Statement:** Find the solution set of \[7 \sin(\theta) = 5 \sin(\theta)\] **Solution Process:** To find the solution set, follow these steps: 1. **Subtract \(5 \sin(\theta)\) from both sides:** \[ 7 \sin(\theta) - 5 \sin(\theta) = 0 \] 2. **Combine like terms:** \[ 2 \sin(\theta) = 0 \] 3. **Divide by 2:** \[ \sin(\theta) = 0 \] The solutions to \(\sin(\theta) = 0\) are the angles where the sine function equals zero. These angles occur at: \[ \theta = n\pi \quad \text{for integer } n \] **Conclusion:** The solution set for the given trigonometric equation \(7 \sin(\theta) = 5 \sin(\theta)\) is: \[ \boxed{\theta = n\pi \text{ for integer } n} \] Understanding how to manipulate and solve basic trigonometric equations is essential in mathematics and can be applied to various fields including physics, engineering, and computer science.
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