Let L be any positive number. Consider the functions sin(x) and cos(x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![6. Let L be any positive number. Consider the functions sin(x) and cos(x) in
L² ([-L, L]) for which values of L are these functions orthogonal to each other
in this space?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd060247b-6254-422b-a1e1-39a452056ba6%2Fa8cbedea-9320-422c-bee3-0b404ebc6b7a%2Fjwrwq26_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Let L be any positive number. Consider the functions sin(x) and cos(x) in
L² ([-L, L]) for which values of L are these functions orthogonal to each other
in this space?
Expert Solution
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Step 1
In this question, we find L for which
the given function
f(x) = sin(x) and g(x) = cos(x) are orthogonal to each other on the space [-L, L]
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