Use the Taylor series to estimate LaTeX: sin(x)s i n ( x ) about LaTeX: a = 0a = 0. Truncate to 6 terms (including terms that simplify to 0). What is the relative error of using this truncated Taylor series to compute the value of LaTeX: sin(\frac{\pi}{4})s i n ( π 4 )?

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Step-by-step explanation:

The Taylor series of a function around a value ("a" is this case) is:

If f(x)=sin(x), the Taylor series will be:

We truncate to 6 term as the question says.

Now, sin(0)=0 and cos(0)=1.

Let's find sin(π/4) using the Taylor series and with the calculator, and then calculate the relative error.

Taylor series

Calculator

The relative error will be:            

I hope it helps you!