# Find a precision for power series $\sin (2x)$ using precision of sin x and cos x

So I have a precision 0,01 for power series $sin x$ and $cos x$. Using the formula $\sin(2x)=2\sin x \cos x$ I need to find the precision for this power series. I know that the answer is 0,04, double sum of the precisions, but i don't know how to explain it using Maclaurin/Taylor and power series.