Chebyshev interpolation of $ln(x+2)$ using $T_3$ on $[-1, 1]$

Question

So finding the points $(x, y)$ is simple. And I find the three points to be interpolated to be:

$(cos \pi/6,1.0529)$ $(cos 3\pi/6,0.6931)$ $(cos 5\pi/6,0.1257)$

But then to construct an interpolating polynomial is where I'm lost. Any indications of what to do next?

The correct solution is $p(x) = -0.1384x^2 + 0.5353x + 0.6931$

Answer 1

So I have solved the problem now, after getting the points to be interpolated you simply just construct a Lagrange interpolation polynomial using these points.