# Decide the linear interpolant

1. Dec 11, 2015

### ForTheGreater

Decide the linear interpolant

f(-pi)=4 f(-pi/2)=5/4 f(0)=1 f(pi/2)=-3/4 f(pi)=0

the function is (1/pi2 ) (x-pi)2 - cos2 (x-pi/2)

Don't know how to do this. I tried lagrange basis functions f(x0)(x1-x)/(x1-x0)+f(x1)(x-x0)/(x1-x0)

But it doesn't turn out right.

The answer for the first interpolant (interval -pi to -pi/2) is: 4-11(x+pi)/(2pi)

2. Dec 13, 2015

### BvU

I sense a contradiction between the problem statement "Decide the interpolant" and the book answer "The answer for the first interpolant ... is...".
Could it be that all you are asked to provide is the four equations "connecting the dots" ?

(The book answer for the first section is the equation of the straight line through $(-\pi, 4)$ and $(-\pi/2, 5/4)$. )

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3. Dec 14, 2015

### ForTheGreater

I have the answer here, it wasn't in the problem.

I'm suppose to give the interpolant in all intervals, or as you put it connect the dots.

Thank you!