Question 8. Consider a vector space V of all continuous functions on -7, 7] with th inner product defined by: (f,g) = | f(x)g(x) dx. For the functions f sin x and = cos x in the space V calculate the following. 1) (f,9), 2) || f ||, 3) || g ||, 4) the angle 0 between the vectors f and g. Hint: for integration use the following trigonometric identities: sin 2x 2 sin x coS x, 2 sin? x = 1– cos 2x, 2 cos? x = 1+ cos 2x.
Question 8. Consider a vector space V of all continuous functions on -7, 7] with th inner product defined by: (f,g) = | f(x)g(x) dx. For the functions f sin x and = cos x in the space V calculate the following. 1) (f,9), 2) || f ||, 3) || g ||, 4) the angle 0 between the vectors f and g. Hint: for integration use the following trigonometric identities: sin 2x 2 sin x coS x, 2 sin? x = 1– cos 2x, 2 cos? x = 1+ cos 2x.
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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taken from my algebra 101 textbook
Transcribed Image Text:Question 8. Consider a vector space V of all continuous functions on [-7, 7| with the
inner product defined by:
(f, 9) = | f(x)g(x) dær.
-T
For the functions f = sin x and g = cos x in the space V calculate the following.
1) (f,g), 2) || f ||, 3) || g ||, 4) the angle 0 between the vectors f and g.
Hint: for integration use the following trigonometric identities:
sin 2x = 2 sin x cos x, 2 sin² x = 1 – cos 2x, 2 cos? x =1+ cos 2x.
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