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.