| Solve the following equation for all eхact degree solutions: 2 sin O cos 0 – V3 cos 0 = 0
| Solve the following equation for all eхact degree solutions: 2 sin O cos 0 – V3 cos 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
![**Problem Statement:**
Solve the following equation for all exact degree solutions:
\[ 2\sin\theta\cos\theta - \sqrt{3}\cos\theta = 0 \]
**Solution Steps:**
1. **Factor the Equation:**
The given equation can be factored as:
\[
\cos\theta (2\sin\theta - \sqrt{3}) = 0
\]
2. **Set Each Factor to Zero:**
We have two cases to solve:
- \(\cos\theta = 0\)
- \(2\sin\theta - \sqrt{3} = 0\)
3. **Solve Each Equation:**
- For \(\cos\theta = 0\), \(\theta = 90^\circ, 270^\circ\).
- For \(2\sin\theta = \sqrt{3}\), solving this gives \(\sin\theta = \frac{\sqrt{3}}{2}\). This occurs at \(\theta = 60^\circ, 120^\circ\).
4. **Combine Solutions:**
The solutions for \(\theta\) in degrees are:
\[
\theta = 60^\circ, 90^\circ, 120^\circ, 270^\circ
\]
This process provides the exact degree solutions for the given trigonometric equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b727f25-8808-4b74-9fb9-f2e74344edb6%2F57f9b0f8-7c1d-4517-ab0a-25f4d1086e40%2F2jiczvm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the following equation for all exact degree solutions:
\[ 2\sin\theta\cos\theta - \sqrt{3}\cos\theta = 0 \]
**Solution Steps:**
1. **Factor the Equation:**
The given equation can be factored as:
\[
\cos\theta (2\sin\theta - \sqrt{3}) = 0
\]
2. **Set Each Factor to Zero:**
We have two cases to solve:
- \(\cos\theta = 0\)
- \(2\sin\theta - \sqrt{3} = 0\)
3. **Solve Each Equation:**
- For \(\cos\theta = 0\), \(\theta = 90^\circ, 270^\circ\).
- For \(2\sin\theta = \sqrt{3}\), solving this gives \(\sin\theta = \frac{\sqrt{3}}{2}\). This occurs at \(\theta = 60^\circ, 120^\circ\).
4. **Combine Solutions:**
The solutions for \(\theta\) in degrees are:
\[
\theta = 60^\circ, 90^\circ, 120^\circ, 270^\circ
\]
This process provides the exact degree solutions for the given trigonometric equation.
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