Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter. 1 cost, sin t, for 0 sts9 V2 r(t) = cost Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. r(t) does not use arc length as a parameter. A description of the curve that uses arc length as a parameter is r(s) = ( for (Type exact answers, using radicals as needed.) O B. r(t) uses arc length as a parameter.
Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter. 1 cost, sin t, for 0 sts9 V2 r(t) = cost Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. r(t) does not use arc length as a parameter. A description of the curve that uses arc length as a parameter is r(s) = ( for (Type exact answers, using radicals as needed.) O B. r(t) uses arc length as a parameter.
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
![**Analysis of Arc Length as a Parameter in Curves**
**Problem Statement:**
Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter.
\[
r(t) = \left\langle \frac{1}{\sqrt{2}} \cos t, \frac{1}{\sqrt{2}} \cos t, \sin t \right\rangle, \text{ for } 0 \leq t \leq 9
\]
**Options:**
- **A.** \( r(t) \) does not use arc length as a parameter. A description of the curve that uses arc length as a parameter is \( r(s) = \left\langle \text{\_\_\_}, \text{\_\_\_}, \text{\_\_\_} \right\rangle \) for \(\text{\_} \leq s \leq \text{\_}\). (Type exact answers, using radicals as needed.)
- **B.** \( r(t) \) uses arc length as a parameter.
**Explanation:**
This problem requires checking if the given parametric equation uses arc length as a parameter. If not, it instructs to convert it to an arc length parameterization. The main task involves calculating the derivative, using it to find arc length, and re-parameterizing accordingly if needed. The boxes in option A are placeholders for exact answers to be filled with the necessary calculations once determined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca46498c-9039-4635-914d-0b10c3becf43%2F32e001c4-cfd9-47d7-9225-14c949065d54%2F89n1cl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Analysis of Arc Length as a Parameter in Curves**
**Problem Statement:**
Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter.
\[
r(t) = \left\langle \frac{1}{\sqrt{2}} \cos t, \frac{1}{\sqrt{2}} \cos t, \sin t \right\rangle, \text{ for } 0 \leq t \leq 9
\]
**Options:**
- **A.** \( r(t) \) does not use arc length as a parameter. A description of the curve that uses arc length as a parameter is \( r(s) = \left\langle \text{\_\_\_}, \text{\_\_\_}, \text{\_\_\_} \right\rangle \) for \(\text{\_} \leq s \leq \text{\_}\). (Type exact answers, using radicals as needed.)
- **B.** \( r(t) \) uses arc length as a parameter.
**Explanation:**
This problem requires checking if the given parametric equation uses arc length as a parameter. If not, it instructs to convert it to an arc length parameterization. The main task involves calculating the derivative, using it to find arc length, and re-parameterizing accordingly if needed. The boxes in option A are placeholders for exact answers to be filled with the necessary calculations once determined.
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
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,
