sin20 + sin e = 0
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°.
Related questions
Question
Find the exact value of the equation on the given interval
![**Equation:**
The given equation is:
\[ \sin 2\theta + \sin \theta = 0 \]
**Explanation:**
This is a trigonometric equation involving sine functions. To solve it, you can use the double-angle identity for sine:
\[ \sin 2\theta = 2 \sin \theta \cos \theta \]
Substituting this identity into the equation gives:
\[ 2 \sin \theta \cos \theta + \sin \theta = 0 \]
Factor out \(\sin \theta\):
\[ \sin \theta (2 \cos \theta + 1) = 0 \]
This results in two possible solutions:
1. \(\sin \theta = 0\)
2. \(2 \cos \theta + 1 = 0\)
**Solution for \(\sin \theta = 0\):**
\(\theta = n\pi\), where \(n\) is an integer.
**Solution for \(2 \cos \theta + 1 = 0\):**
\(\cos \theta = -\frac{1}{2}\)
\(\theta = \pm \frac{2\pi}{3} + 2n\pi\), where \(n\) is an integer.
Therefore, the solutions are \(\theta = n\pi\) and \(\theta = \pm \frac{2\pi}{3} + 2n\pi\).
No graphs or diagrams are included in this content.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F959e4537-60e0-4bbe-84b3-df36ad9248f0%2F74e5d8ad-0331-4f7b-8077-45cf9d78a277%2Fyy2dguw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equation:**
The given equation is:
\[ \sin 2\theta + \sin \theta = 0 \]
**Explanation:**
This is a trigonometric equation involving sine functions. To solve it, you can use the double-angle identity for sine:
\[ \sin 2\theta = 2 \sin \theta \cos \theta \]
Substituting this identity into the equation gives:
\[ 2 \sin \theta \cos \theta + \sin \theta = 0 \]
Factor out \(\sin \theta\):
\[ \sin \theta (2 \cos \theta + 1) = 0 \]
This results in two possible solutions:
1. \(\sin \theta = 0\)
2. \(2 \cos \theta + 1 = 0\)
**Solution for \(\sin \theta = 0\):**
\(\theta = n\pi\), where \(n\) is an integer.
**Solution for \(2 \cos \theta + 1 = 0\):**
\(\cos \theta = -\frac{1}{2}\)
\(\theta = \pm \frac{2\pi}{3} + 2n\pi\), where \(n\) is an integer.
Therefore, the solutions are \(\theta = n\pi\) and \(\theta = \pm \frac{2\pi}{3} + 2n\pi\).
No graphs or diagrams are included in this content.
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