find the soluton set of 7sine il | = 5 sin e

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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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.
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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