Generalizing Example 2.17(c), by a trigonometric polynomial of degree

in the powers of the sine and cosine functions up to degree n. degree n.
(a) Use formula (3.86) to prove that any trigonometric polynomial of degree

(b) Prove that any trigonometric polynomial of degree ‰¤ n can be written as a real linear combination of the trigonometric functions 1. cosθ, sinθ, cos2θ, sin2θ,.. .cos«Î¸, sin «Î¸.
(c) Write out the following trigonometric polynomials in both of the preceding forms:
(i) cos2θ
(ii) cos θ sin θ
(iii) cos3θ
(iv) sin4θ
(v) cos2 θ sin2 θ

Transcribed Image Text:

T(x) = 2 Cjk (cos 6) (sin 0 )* Osj+k sn