Solve the equation √3+5 cos 0 = 3 cos. Express the answer in radian measure. * Student can enter max 2000 characters ΧΕ BIU EΞΩ Use the paperclip button below to attach files.
Solve the equation √3+5 cos 0 = 3 cos. Express the answer in radian measure. * Student can enter max 2000 characters ΧΕ BIU EΞΩ Use the paperclip button below to attach files.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Solving the Equation
**Problem:** Solve the equation \( \sqrt{3} + 5\cos{\theta} = 3\cos{\theta} \). Express the answer in radian measure.
---
### Instructions:
1. **Step-by-Step Solution**:
- Start by isolating the cosine term.
- Simplify the equation where necessary.
- Solve for \(\theta\) considering the unit circle and the range of cosine function values.
2. **Student Response Area**:
- You can enter your step-by-step solution in the text input area provided below.
- Remember to check your work thoroughly and ensure your final answer is in radians.
**Note**: Students can enter a maximum of 2000 characters.
---
**Attachment Instructions**:
- If you need to attach files, use the paperclip button below to upload your documents or additional work.
---
### Example of Simplifying the Given Equation:
Given:
\[ \sqrt{3} + 5\cos{\theta} = 3\cos{\theta} \]
1. Combine like terms on the right-hand side:
\[ \sqrt{3} = 3\cos{\theta} - 5\cos{\theta} \]
2. Simplify the equation:
\[ \sqrt{3} = -2\cos{\theta} \]
3. Solve for \(\cos{\theta}\):
\[ \cos{\theta} = -\frac{\sqrt{3}}{2} \]
4. Determine \(\theta\) in radians:
\[ \theta = \frac{5\pi}{6}, \; \theta = \frac{7\pi}{6} \]
These are the angles where cosine equals \(-\frac{\sqrt{3}}{2}\).
---
**Graph/Diagram Explanation:**
There are no graphs or diagrams in the given image. The image displays a keyboard below a computer screen showing a mathematical equation and text instructions indicating where and how a student should type their response, with character limits mentioned.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcccb93a5-bda7-4c84-b750-51d9219067a4%2Fd73e15e1-bd60-413b-90c7-4bc39e90aa02%2Fqoy4nii_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving the Equation
**Problem:** Solve the equation \( \sqrt{3} + 5\cos{\theta} = 3\cos{\theta} \). Express the answer in radian measure.
---
### Instructions:
1. **Step-by-Step Solution**:
- Start by isolating the cosine term.
- Simplify the equation where necessary.
- Solve for \(\theta\) considering the unit circle and the range of cosine function values.
2. **Student Response Area**:
- You can enter your step-by-step solution in the text input area provided below.
- Remember to check your work thoroughly and ensure your final answer is in radians.
**Note**: Students can enter a maximum of 2000 characters.
---
**Attachment Instructions**:
- If you need to attach files, use the paperclip button below to upload your documents or additional work.
---
### Example of Simplifying the Given Equation:
Given:
\[ \sqrt{3} + 5\cos{\theta} = 3\cos{\theta} \]
1. Combine like terms on the right-hand side:
\[ \sqrt{3} = 3\cos{\theta} - 5\cos{\theta} \]
2. Simplify the equation:
\[ \sqrt{3} = -2\cos{\theta} \]
3. Solve for \(\cos{\theta}\):
\[ \cos{\theta} = -\frac{\sqrt{3}}{2} \]
4. Determine \(\theta\) in radians:
\[ \theta = \frac{5\pi}{6}, \; \theta = \frac{7\pi}{6} \]
These are the angles where cosine equals \(-\frac{\sqrt{3}}{2}\).
---
**Graph/Diagram Explanation:**
There are no graphs or diagrams in the given image. The image displays a keyboard below a computer screen showing a mathematical equation and text instructions indicating where and how a student should type their response, with character limits mentioned.
---
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