We've defined, for example, and at this stage the value of x could be any number. Recall that x was originally . So, looking at the values that can take on, should be of particular interest.
Some ideas to get you started: - Look at the constant terms - Look at the coefficient of in . - What coefficients are zero, and when? - Look for symmetries in the graphs of the Chebyshev polynomials. How are symmetries related to the coefficients?
The best way to prove many of the properties of Chebyshev polynomials is by
induction.
and at this stage the value of x could be any number. Recall that x was originally 
. So, looking at the values that 
can take on, 
should be of particular interest.
in 
.
