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Introduce Sec 2 trig identity
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Conclusion Sec 2 trig identity
**Therefore, the estimated value at x = 0 is 0.** This example showcases interpolation with unevenly spaced points. The process remains the same, but the resulting polynomial will be influenced by the spacing between the data points. Even though the x-values are not evenly spaced, **Lagrange Interpolation** still provides a method to find a polynomial that passes through all given points. The Lagrange basis polynomials are calculated to ensure that they are 1 at their corresponding x-values and 0 at all other x-values, enabling the interpolation polynomial to match the data points exactly. The estimated value at *x* = 0, *P*(0) = 0, represents a point on the curve that fits the three data points. Unevenly spaced points are common in real-world data, making this example particularly relevant.
