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

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

01:37

Wen Zheng

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

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Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

02:28

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

07:47

Use the Maclaurin series f…

01:10

05:14

04:05

02:09

05:44

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

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