Write a Matlab function to compute f(x) = 1 - cos(x) for inputs in the range...

 

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Write a Matlab function to compute f(x) = 1 - cos(x) for inputs in the range -1 <x< 1 with fractional error under 100. Check your function by verifying that, to 14 significant digits, it returns f(10-4 ) = 4.9999999958333 × 10-9 and f(0.9) = 0.37839003172934. Hint: Subtracting 1 - cos(x) directly incurs subtractive cancellation when x is close to 0, but for such values of x, the truncation error from using the first few terms of the Taylor series of cos(x) with a = 0 and cancelling out the 1 analytically is very small. Write a Matlab function to compute f(x) = 1 - cos(x) for inputs in the range -1 <x< 1 with fractional error under 100. Check your function by verifying that, to 14 significant digits, it returns f(10-4 ) = 4.9999999958333 × 10-9 and f(0.9) = 0.37839003172934. Hint: Subtracting 1 - cos(x) directly incurs subtractive cancellation when x is close to 0, but for such values of x, the truncation error from using the first few terms of the Taylor series of cos(x) with a = 0 and cancelling out the 1 analytically is very small.

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