What have you tried? If nothing, then why not?
Easy enough to build a Chebychev polynomial, using the standard recursion relations. Wikipedia will surely give them, and I know that sufficient information can be found in Abramowitz and Stegun, because I wrote tools based on that long ago. My copy of Abramowitz and Stegun is so well used that I put tabs in it at a few useful pages. (A useful text.) Then you just make it into a function of theta, as you wish. So just create a function handle.
Probably easier yet is to download the chebfun toolbox, which will probably make it easy to solve that problem. So 2 simple lines of code.
p3 = chebpoly(3);
pfun = @(theta) p3(sin(theta));
pfun(.5)
ans =
-0.99749
Or, if you wanted it for a general value of n, not fixed in advance as I did, then just write a function m-file.
