ind the exact values of s in the interval [0,2x) that satisfy the given condition cos 1.2
ind the exact values of s in the interval [0,2x) that satisfy the given condition cos 1.2
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°.
Related questions
Question
Find the exact values of s in the interval [0,2π) that satisfy the condition, cos s = 1 / 2.
![**Problem Statement:**
Find the exact values of \( s \) in the interval \([0, 2\pi)\) that satisfy the given condition:
\[ \cos\left(\frac{2s}{5}\right) = \frac{1}{2} \]
**Solution Explanation:**
This trigonometric problem requires us to find the values of \( s \) that meet the condition specified. Let's break down the solution step-by-step.
1. **Rewrite the Condition:**
We start from the given equation:
\[
\cos\left(\frac{2s}{5}\right) = \frac{1}{2}
\]
2. **Identify the Angles:**
Recall that the cosine of \( \frac{\pi}{3} \) (or \(60^\circ\)) is \( \frac{1}{2} \). Therefore:
\[
\frac{2s}{5} = \frac{\pi}{3} + 2k\pi \quad \text{or} \quad \frac{2s}{5} = -\frac{\pi}{3} + 2k\pi
\]
for any integer \( k \).
3. **Solve for \( s \):**
\[
s = \frac{5}{2}\left(\frac{\pi}{3} + 2k\pi\right) \quad \text{or} \quad s = \frac{5}{2}\left(-\frac{\pi}{3} + 2k\pi\right)
\]
4. **Simplify:**
\[
s = \frac{5\pi}{6} + 5k\pi \quad \text{or} \quad s = -\frac{5\pi}{6} + 5k\pi
\]
5. **Consider the Interval \([0, 2\pi)\):**
We now need the solutions for \( s \) to be within \([0, 2\pi)\).
For \(\frac{5\pi}{6} + 5k\pi :\)
\[
0 \leq \frac{5\pi}{6} + 5k\pi < 2\pi \implies k = 0 \rightarrow s = \frac{5\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1dbff557-c987-45fc-8dd6-6084416c9157%2F1732b001-7ca9-4a7c-a821-c624611d0743%2Fao1l3mr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the exact values of \( s \) in the interval \([0, 2\pi)\) that satisfy the given condition:
\[ \cos\left(\frac{2s}{5}\right) = \frac{1}{2} \]
**Solution Explanation:**
This trigonometric problem requires us to find the values of \( s \) that meet the condition specified. Let's break down the solution step-by-step.
1. **Rewrite the Condition:**
We start from the given equation:
\[
\cos\left(\frac{2s}{5}\right) = \frac{1}{2}
\]
2. **Identify the Angles:**
Recall that the cosine of \( \frac{\pi}{3} \) (or \(60^\circ\)) is \( \frac{1}{2} \). Therefore:
\[
\frac{2s}{5} = \frac{\pi}{3} + 2k\pi \quad \text{or} \quad \frac{2s}{5} = -\frac{\pi}{3} + 2k\pi
\]
for any integer \( k \).
3. **Solve for \( s \):**
\[
s = \frac{5}{2}\left(\frac{\pi}{3} + 2k\pi\right) \quad \text{or} \quad s = \frac{5}{2}\left(-\frac{\pi}{3} + 2k\pi\right)
\]
4. **Simplify:**
\[
s = \frac{5\pi}{6} + 5k\pi \quad \text{or} \quad s = -\frac{5\pi}{6} + 5k\pi
\]
5. **Consider the Interval \([0, 2\pi)\):**
We now need the solutions for \( s \) to be within \([0, 2\pi)\).
For \(\frac{5\pi}{6} + 5k\pi :\)
\[
0 \leq \frac{5\pi}{6} + 5k\pi < 2\pi \implies k = 0 \rightarrow s = \frac{5\
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