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Problem 49 Medium Difficulty

Use the Maclaurin series for $ \cos x $ to compute $ \cos 5^o $ correct to five decimal places.

Answer

$\cos 5^{\circ} \approx 0.99619$ (calculator gives 0.996194696$)$

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Video Transcript

first problem. We want to, um, use the MacLaurin series for cosine X. So we know that the co Sin X MacLaurin series is equal to the some from an equal zero to infinity of negative one to the end of X to the two n over two and factorial. Now we want to convert five degrees to raid Ian's. So five degrees. If we convert it to raid IANS, it's going to give us approximately 0.87266463 Um, and what we have to do now is just one minus this value. We square it and put it over two factorial because there's just two terms. Um, And when we use this in the calculator, we get, um, that's approximately going to be 0.99619 And sure enough, if we do it in a calculator, we'll get something very similar