Let B= {1, cost, cos?t, .. cos t} and C={1, cost, cos 2t, ... , cos 61). Assume the following trigonometric identities. cos 2t = - 1+2 cos²t cos 3t = - 3 cost+ 4 cost cos 4t = 1-8 cos t+8 cos t cos 5t = 5 cost- 20 cost+ 16 cos St cos 6t = - 1+ 18 cos²t- 48 cos t+ 32 cos ºt Let H be the subspace of functions spanned by the functions in B. Then Bis a basis for H. Complete parts (a) and (b). a. Write the B-coordinate vectors of the vectors in C as the columns of a matrix P, and use them to show that C is a linearly independent set in H. P=O
Let B= {1, cost, cos?t, .. cos t} and C={1, cost, cos 2t, ... , cos 61). Assume the following trigonometric identities. cos 2t = - 1+2 cos²t cos 3t = - 3 cost+ 4 cost cos 4t = 1-8 cos t+8 cos t cos 5t = 5 cost- 20 cost+ 16 cos St cos 6t = - 1+ 18 cos²t- 48 cos t+ 32 cos ºt Let H be the subspace of functions spanned by the functions in B. Then Bis a basis for H. Complete parts (a) and (b). a. Write the B-coordinate vectors of the vectors in C as the columns of a matrix P, and use them to show that C is a linearly independent set in H. P=O
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 40E
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