The sine functions are defined as

while Sj(x) = S0(x - j h) whenever h > 0 and j is an integer. We will interpolate a function /(x) at the mesh points Xj = jh, j = 0,... ,«, by a linear combination of sine functions: S(.v) = c0S0(x) cnSn (x). What are the coefficients Cj? Graph and discuss the accuracy of the sine in- terpolant for the functions x2 and ½ - | x - ½| on the interval [0, 1 ] using h = .25, .1 and .025.

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So(x) = sin(πχ/h)