Solve the equation 4√2+8 cosx=0. Write the numbers using integers or simplified fractions. Part: 0/2 Part 1 of 2 (a) Over the interval [0,2). The solution set is 0,0.... Л X 0/0 G
Solve the equation 4√2+8 cosx=0. Write the numbers using integers or simplified fractions. Part: 0/2 Part 1 of 2 (a) Over the interval [0,2). The solution set is 0,0.... Л X 0/0 G
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter3: Multi-step Equations And Inequalities
Section: Chapter Questions
Problem 11PTTS
Related questions
Question
![### Solving Trigonometric Equations
**Problem Statement:**
Solve the equation \( 4\sqrt{2} + 8\cos{x} = 0 \). Write the numbers using integers or simplified fractions.
**Part 1 of 2:**
(a) Over the interval \([0, 2\pi)\):
The solution set is:
\[ \boxed{} \]
**Explanation:**
In this problem, you are tasked with solving a trigonometric equation over a specified interval. Here is a step-by-step approach to solve the equation \( 4\sqrt{2} + 8\cos{x} = 0 \):
1. **Isolate the Trigonometric Function:**
\[ 4\sqrt{2} + 8\cos{x} = 0 \]
\[ 8\cos{x} = -4\sqrt{2} \]
\[ \cos{x} = \frac{-4\sqrt{2}}{8} \]
\[ \cos{x} = -\frac{\sqrt{2}}{2} \]
2. **Determine the Angles:**
Recall the unit circle values. The cosine of \( x \) is \( -\frac{\sqrt{2}}{2} \) at specific angles within the interval \([0, 2\pi)\):
\[ x = \frac{3\pi}{4} \text{ and } x = \frac{5\pi}{4} \]
Thus, the solution set within the interval \([0, 2\pi)\) is:
\[ x = \left\{ \frac{3\pi}{4}, \frac{5\pi}{4} \right\} \]
Please enter these values in the solution set box.
**Interactive Elements:**
- The interface provides you with an input box to type the solution.
- There are mathematical symbols available for ease of entry, such as \(\pi\), fraction structures, and more.
Once you have entered the solutions in the provided box, you can proceed to the next part by clicking the "Next Part" button.
---
*Note: This transcription is intended for educational purposes on an educational website and includes step-by-step guidance for solving the given trigonometric equation.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe92e694a-8dce-4f5c-a0b3-7db66cedb1e5%2F899ced0d-6c4d-4d99-ba08-7afd2de68dbc%2Fc9ysex_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Trigonometric Equations
**Problem Statement:**
Solve the equation \( 4\sqrt{2} + 8\cos{x} = 0 \). Write the numbers using integers or simplified fractions.
**Part 1 of 2:**
(a) Over the interval \([0, 2\pi)\):
The solution set is:
\[ \boxed{} \]
**Explanation:**
In this problem, you are tasked with solving a trigonometric equation over a specified interval. Here is a step-by-step approach to solve the equation \( 4\sqrt{2} + 8\cos{x} = 0 \):
1. **Isolate the Trigonometric Function:**
\[ 4\sqrt{2} + 8\cos{x} = 0 \]
\[ 8\cos{x} = -4\sqrt{2} \]
\[ \cos{x} = \frac{-4\sqrt{2}}{8} \]
\[ \cos{x} = -\frac{\sqrt{2}}{2} \]
2. **Determine the Angles:**
Recall the unit circle values. The cosine of \( x \) is \( -\frac{\sqrt{2}}{2} \) at specific angles within the interval \([0, 2\pi)\):
\[ x = \frac{3\pi}{4} \text{ and } x = \frac{5\pi}{4} \]
Thus, the solution set within the interval \([0, 2\pi)\) is:
\[ x = \left\{ \frac{3\pi}{4}, \frac{5\pi}{4} \right\} \]
Please enter these values in the solution set box.
**Interactive Elements:**
- The interface provides you with an input box to type the solution.
- There are mathematical symbols available for ease of entry, such as \(\pi\), fraction structures, and more.
Once you have entered the solutions in the provided box, you can proceed to the next part by clicking the "Next Part" button.
---
*Note: This transcription is intended for educational purposes on an educational website and includes step-by-step guidance for solving the given trigonometric equation.*
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Transcribed Image Text:Solve the equation 4√√2+8 cos x=0. Write the numbers using integers or simplified fractions.
Part: 0/2
Part 1 of 2
(a) Over the interval [0,2).
3π 5π
The solution set is
믐
0,0,...
4
4
3
Part: 1 / 2
Part 2 of 2
(b) Over the set of real numbers. Use n, where n is an integer.
X=
The general solution is {x|x=₁x=}
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