Step 5: Solve f(x) = 0 ANALYTICALLY. That said, you may need the use of a calculator at some point if our roots are not rational. If that's the case, make sure you provide a "calculator ready answer," then use nverse trig and calculator to solve. Be sure to find two solutions, f(x) = 8sin (x - ²π) - 4
Step 5: Solve f(x) = 0 ANALYTICALLY. That said, you may need the use of a calculator at some point if our roots are not rational. If that's the case, make sure you provide a "calculator ready answer," then use nverse trig and calculator to solve. Be sure to find two solutions, f(x) = 8sin (x - ²π) - 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Answer this question with all the steps and parts to the question, please show all work and steps. DO NOT USE A GRAPHING SOFTWARE ALL WORK MUST BE DONE ANALYTICALLY. Thank you.
![### Step 5: Solve \( f(x) = 0 \) ANALYTICALLY
That said, you may need the use of a calculator at some point if your roots are not rational. If that's the case, make sure you provide a "calculator ready answer," then use inverse trig and calculator to solve. **Be sure to find two solutions.**
Given function:
\[ f(x) = 8 \sin\left(x - \frac{2}{5} \pi \right) - 4 \]
1. **Rewrite with function set to zero:**
\[ 0 = 8 \sin\left(x - \frac{2}{5} \pi \right) - 4 \]
2. **Solve for the sine function:**
\[ 4 = 8 \sin\left(x - \frac{2}{5} \pi \right) \]
\[ \sin\left(x - \frac{2}{5} \pi \right) = \frac{1}{2} \]
3. **Calculate the general solutions for \( \sin \theta = \frac{1}{2} \):**
\[ \theta = \frac{\pi}{6}, ~\theta = \pi - \frac{\pi}{6} = \frac{5\pi}{6} \]
4. **Find \( x \) by reverting the shift applied:**
\[ x - \frac{2}{5} \pi = \frac{\pi}{6} \rightarrow x = \frac{\pi}{6} + \frac{2}{5} \pi = \frac{5\pi}{15} + \frac{6\pi}{15} = \frac{11\pi}{15} \]
\[ x - \frac{2}{5} \pi = \frac{5\pi}{6} \rightarrow x = \frac{5\pi}{6} + \frac{2}{5} \pi = \frac{25\pi}{30} + \frac{12\pi}{30} = \frac{37\pi}{30} \]
Thus, the two solutions are:
\[ x = \frac{11\pi}{15} \]
\[ x = \frac{37\pi}{30} \]
This process will give you the two solutions analytically. If any part](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1cfa5eb8-7836-4ef7-ac0c-0e26ee4fbf03%2Fdecc71d0-7bdc-4b14-9bce-924d0a4b6f9c%2Fa6k6ye_processed.png&w=3840&q=75)
Transcribed Image Text:### Step 5: Solve \( f(x) = 0 \) ANALYTICALLY
That said, you may need the use of a calculator at some point if your roots are not rational. If that's the case, make sure you provide a "calculator ready answer," then use inverse trig and calculator to solve. **Be sure to find two solutions.**
Given function:
\[ f(x) = 8 \sin\left(x - \frac{2}{5} \pi \right) - 4 \]
1. **Rewrite with function set to zero:**
\[ 0 = 8 \sin\left(x - \frac{2}{5} \pi \right) - 4 \]
2. **Solve for the sine function:**
\[ 4 = 8 \sin\left(x - \frac{2}{5} \pi \right) \]
\[ \sin\left(x - \frac{2}{5} \pi \right) = \frac{1}{2} \]
3. **Calculate the general solutions for \( \sin \theta = \frac{1}{2} \):**
\[ \theta = \frac{\pi}{6}, ~\theta = \pi - \frac{\pi}{6} = \frac{5\pi}{6} \]
4. **Find \( x \) by reverting the shift applied:**
\[ x - \frac{2}{5} \pi = \frac{\pi}{6} \rightarrow x = \frac{\pi}{6} + \frac{2}{5} \pi = \frac{5\pi}{15} + \frac{6\pi}{15} = \frac{11\pi}{15} \]
\[ x - \frac{2}{5} \pi = \frac{5\pi}{6} \rightarrow x = \frac{5\pi}{6} + \frac{2}{5} \pi = \frac{25\pi}{30} + \frac{12\pi}{30} = \frac{37\pi}{30} \]
Thus, the two solutions are:
\[ x = \frac{11\pi}{15} \]
\[ x = \frac{37\pi}{30} \]
This process will give you the two solutions analytically. If any part
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
