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Mathematics

The Role of Taylor Series in Approximation

Quick fact

The Taylor series for sin(x) is so accurate that with just 10 terms, it can approximate sin(x) to within 10^-28 for x up to 10!

Why this is interesting

You’ve probably used a calculator to find sin(0.5) without thinking about it. But how does the calculator know the answer? It likely uses a trick that lets it compute almost any function using only addition, multiplication, and division—a trick called the Taylor series.