Use a calculator to solve the equation on the interval 

left bracket 0 comma 2 pi right parenthesis[0,2π).

cosine x equals negative four seventhscosx=−47

Question content area bottom

Part 1

What are the solutions in the interval 

left bracket 0 comma 2 pi right parenthesis[0,2π)​? 

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

xequals=enter your response here

​(Type your answer in radians. Round to four decimal places as needed. Use a comma to separate answers as​ needed.)

The solutions to the equation \(\cos(x) = -\frac{4}{7}\) within the interval \([0, 2\pi)\) are:

\[ x = 2.1790 \, \text{radians}, \, 4.1041 \, \text{radians} \]

Let me know if you need more details or have any other questions!

Here are 8 related questions you might consider:
1. How does the cosine function differ from the sine function in terms of symmetry?
2. What is the range of the cosine function?
3. How does the cosine function behave within one complete cycle \([0, 2\pi)\)?
4. What are the general solutions for \(\cos(x) = a\)?
5. How can the unit circle be used to visualize solutions for \(\cos(x) = a\)?
6. What key properties distinguish the cosine function from other trigonometric functions?
7. How would the solutions change if \(\cos(x)\) equaled a different value?
8. What are some real-life applications of solving trigonometric equations?

**Tip:** For cosine equations, remember that the function is even and periodic, so the solutions are symmetric about the y-axis.

Learn how to solve the trigonometric equation cos(x) = -4/7 within the interval [0, 2π). Find detailed solutions and understand the behavior of the cosine function. Suitable for high school students studying trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation