Example 5.  Find the roots of the Chebyshev polynomial.

Explore Solution 5.

Aside.  If you are curious why  ,  then the results of Section 5.5 can be used to clear up this matter.

Aside.  The Chebyshev polynomials can be defined recursively, and trigonometric identities can be used to establish that .  For details, see the article:  A Note on Identities for  cos nt  via Chebyshev Polynomials, by John Mathews, Mathematics and Computer Education Journal, V.22, No. 3, Fall 1988, pp. 192-193.

(c) 2006 John H. Mathews, Russell W. Howell