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The maclaurin series expansion for sin(x) is: sin(x)=x−x33!+x55!−x77!+x99!−.... starting with simplest version sin(x)=x, add terms one at time to estimate sin(π/8). after each new term is added, compute the true and approximate percent relative errors. add terms until value of approximate error estimation error falls bellow an error criterion conforming to two significant figures.

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sqdancefan
In the attached table, the true error (a) and the relative error (r) are multiplied by 100. The answer will be correct to 2 significant figures when these are below 0.5 and 1.3, respectively.

This occurs when the second term is added to the series.

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For reference, sin(π/8) = 0.382683432365...
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