The thing being learned here are (a,b) and you do that using data (x,y). We can rewrite our input to be of the form z = {sin(x), x^2} and then now we have the m

The thing being learned here are (a,b) and you do that using data (x,y). We can rewrite our input to be of the form z = {sin(x), x^2} and then now we have the model y = a z_1 + b z_2 which is now obviously linear in z. Since x is given to us and z is just a function of x, nothing strange is happening here. Just manipulating the data.