2 sin 0- sin 0 = 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
![The equation shown is:
\[
\sqrt{2} \sin^2 \theta - \sin \theta = 0
\]
This is a trigonometric equation where \(\theta\) is the variable. To solve for \(\theta\), one common approach is to factor the equation:
1. Factor out \(\sin \theta\):
\[
\sin \theta (\sqrt{2} \sin \theta - 1) = 0
\]
2. Set each factor to zero:
\[
\sin \theta = 0 \quad \text{or} \quad \sqrt{2} \sin \theta - 1 = 0
\]
3. Solve each equation:
- For \(\sin \theta = 0\), \(\theta = n\pi\), where \(n\) is an integer.
- For \(\sqrt{2} \sin \theta = 1\), \(\sin \theta = \frac{1}{\sqrt{2}}\). This is where \(\theta = \frac{\pi}{4} + 2k\pi\) or \(\theta = \frac{3\pi}{4} + 2k\pi\), where \(k\) is an integer.
These solutions encompass all possible \(\theta\) values that satisfy the original equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc16206f4-19bf-423e-ba9e-756d199d055d%2Fb7756e24-1345-4bcb-b799-afcf7f867052%2Fxn52fga_processed.png&w=3840&q=75)
Transcribed Image Text:The equation shown is:
\[
\sqrt{2} \sin^2 \theta - \sin \theta = 0
\]
This is a trigonometric equation where \(\theta\) is the variable. To solve for \(\theta\), one common approach is to factor the equation:
1. Factor out \(\sin \theta\):
\[
\sin \theta (\sqrt{2} \sin \theta - 1) = 0
\]
2. Set each factor to zero:
\[
\sin \theta = 0 \quad \text{or} \quad \sqrt{2} \sin \theta - 1 = 0
\]
3. Solve each equation:
- For \(\sin \theta = 0\), \(\theta = n\pi\), where \(n\) is an integer.
- For \(\sqrt{2} \sin \theta = 1\), \(\sin \theta = \frac{1}{\sqrt{2}}\). This is where \(\theta = \frac{\pi}{4} + 2k\pi\) or \(\theta = \frac{3\pi}{4} + 2k\pi\), where \(k\) is an integer.
These solutions encompass all possible \(\theta\) values that satisfy the original equation.
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