10. 3cot (x) =-L

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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Question

B) Solve the equation for 0 < or equal to x < or equal to 2pi

C) find all solutions to the equation in radians

Must be done WITHOUT A CALCULATOR. there is only one answer. answer choices are on the first image

10. \(\sqrt{3} \cot(x) = -1\)

This equation represents a trigonometric identity involving the cotangent function. To solve for \(x\), you'll need to understand basic trigonometric concepts and how to manipulate such equations. The equation implies finding the angle \(x\) where the cotangent is \(-\frac{1}{\sqrt{3}}\), considering the properties and periodicity of the trigonometric functions.
Transcribed Image Text:10. \(\sqrt{3} \cot(x) = -1\) This equation represents a trigonometric identity involving the cotangent function. To solve for \(x\), you'll need to understand basic trigonometric concepts and how to manipulate such equations. The equation implies finding the angle \(x\) where the cotangent is \(-\frac{1}{\sqrt{3}}\), considering the properties and periodicity of the trigonometric functions.
### Problem 8: Problem 6.3.10 b and c

#### Option A
- **b:** \(\frac{5\pi}{6}, \frac{11\pi}{6}\)  
- **c:** \(\frac{5\pi}{6} + k\pi\)  

#### Option B
- **b:** \(\frac{\pi}{3}, \frac{4\pi}{3}\)
- **c:** \(\frac{\pi}{3} + k\pi\)

#### Option C
- **b:** \(\frac{2\pi}{3}, \frac{5\pi}{3}\)  
- **c:** \(\frac{2\pi}{3} + k\pi\)  

#### Option D
- **b:** \(\frac{\pi}{3}, \frac{4\pi}{3}\)  
- **c:** \(\frac{\pi}{3} + 2k\pi, \frac{4\pi}{3} + 2k\pi\)

#### Option E
- **b:** \(\frac{2\pi}{3}, \frac{4\pi}{3}\)  
- **c:** \(\frac{2\pi}{3} + k\pi\)  

### Explanation
Each option provides solutions \(b\) and \(c\) in terms of \(\pi\), indicating specific angles or periodic solutions, where \(k\) denotes an integer representing the multiple of the periodic interval.
Transcribed Image Text:### Problem 8: Problem 6.3.10 b and c #### Option A - **b:** \(\frac{5\pi}{6}, \frac{11\pi}{6}\) - **c:** \(\frac{5\pi}{6} + k\pi\) #### Option B - **b:** \(\frac{\pi}{3}, \frac{4\pi}{3}\) - **c:** \(\frac{\pi}{3} + k\pi\) #### Option C - **b:** \(\frac{2\pi}{3}, \frac{5\pi}{3}\) - **c:** \(\frac{2\pi}{3} + k\pi\) #### Option D - **b:** \(\frac{\pi}{3}, \frac{4\pi}{3}\) - **c:** \(\frac{\pi}{3} + 2k\pi, \frac{4\pi}{3} + 2k\pi\) #### Option E - **b:** \(\frac{2\pi}{3}, \frac{4\pi}{3}\) - **c:** \(\frac{2\pi}{3} + k\pi\) ### Explanation Each option provides solutions \(b\) and \(c\) in terms of \(\pi\), indicating specific angles or periodic solutions, where \(k\) denotes an integer representing the multiple of the periodic interval.
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