Decide the linear interpolant

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)


Science Advisor
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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)##. )

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!

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