1. ## Interpolation

a) Find the function P(x) = a + bcos(pi x) + csin(pi x) which interpolates the data
x | 0 0.5 1
y | 2 5 4

b) Find the quadratic plynomial interpolating this data

2. Originally Posted by jzellt
a) Find the function P(x) = a + bcos(pi x) + csin(pi x) which interpolates the data
x | 0 0.5 1
y | 2 5 4
At a minimum plugging the data into the interpolating form will give you three simultaneous linear equations in three unknowns which you should be able to solve.

For the first point this gives:

$2=a+b \cos(0) + c \sin(0)$

or:

$2=a+b$

CB