Problem 6.3.30 Use radians instead of degrees. 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°.
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Question
please answer this WITHOUT A CALCULATOR. there is only one answer. instructions and answer choices are on the images
Transcribed Image Text:**Problem 9: Problem 6.3.30**
Use radians instead of degrees. \(0 \leq x < 2\pi\)
Options:
- **A.** \(\pi\)
- **B.** \(\frac{\pi}{2}, \frac{3\pi}{2}, \pi\)
- **C.** \(\frac{\pi}{2}, \frac{3\pi}{2}\)
- **D.** \(0, \pi\)
- **E.** No solution.
![**Problem 30:** Solve the equation \( \cos^2(x) = -\cos(x) \).
This mathematical equation involves trigonometric identities. It requires solving using algebraic manipulation and trigonometric concepts to find the values of \( x \) that satisfy the equation. Here's how you might approach solving it:
1. **Rearrange the equation:**
\[
\cos^2(x) + \cos(x) = 0
\]
2. **Factor the equation:**
\[
\cos(x)(\cos(x) + 1) = 0
\]
3. **Solve each factor:**
- For \(\cos(x) = 0\), \( x = \frac{\pi}{2} + n\pi \), where \( n \) is an integer.
- For \(\cos(x) + 1 = 0\), \(\cos(x) = -1\), which gives \( x = \pi + 2n\pi \), where \( n \) is an integer.
These solutions give the general \( x \)-values where the original equation holds true.
**Note:** Ensure your solutions are within the required domain of the problem if specified.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3348a9c-7c7d-4999-b36a-cd8f5af69dd1%2F75c60093-1dde-48db-9be1-f40f13fa0b06%2Fimz3z47_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 30:** Solve the equation \( \cos^2(x) = -\cos(x) \).
This mathematical equation involves trigonometric identities. It requires solving using algebraic manipulation and trigonometric concepts to find the values of \( x \) that satisfy the equation. Here's how you might approach solving it:
1. **Rearrange the equation:**
\[
\cos^2(x) + \cos(x) = 0
\]
2. **Factor the equation:**
\[
\cos(x)(\cos(x) + 1) = 0
\]
3. **Solve each factor:**
- For \(\cos(x) = 0\), \( x = \frac{\pi}{2} + n\pi \), where \( n \) is an integer.
- For \(\cos(x) + 1 = 0\), \(\cos(x) = -1\), which gives \( x = \pi + 2n\pi \), where \( n \) is an integer.
These solutions give the general \( x \)-values where the original equation holds true.
**Note:** Ensure your solutions are within the required domain of the problem if specified.
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