Interpolation Given the data points xi yi 0 1 pi2 15 what is

Interpolation Given the data points x_i y_i 0 1 pi/2 15 what is the coefficient beta in the interpolant f(x) = alpha 1 + beta sin (x) ?

Solution

f(x) = ₁ + sin(x)

Given the data points

x_i

y_i

0

1

/2

15

f(x_i) = y_i

Then, f(0) = 1 implies that, ₁ + sin(0) = 1

Or, ₁ = 1                               We know that, sin(0) = 0

Hence, f(x) = 1 + sin(x)

Now, f(/2) = 15 implies that, 1 + sin(/2) = 15

Or, 1 + = 15                      We know that, sin(/2) = 1

Or, = 14

Therefore, the coefficient in the interpolant f(x) = ₁ + sin(x) is 14. (Answer)

xi	yi
0	1
/2	15