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Evaluate the given functions by using the series developed in the examples of this section.$$\sin 33^{\circ}$$

Calculus 2 / BC

Chapter 30

Expansion of Functions in Series

Section 5

Taylor Series

Series

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Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

00:19

For the following exercise…

00:39

07:05

Use a calculator to find t…

00:16

Evaluate the following fun…

01:41

Use power series operation…

06:44

Find the Maclaurin series …

08:10

In the following exercises…

01:07

00:26

Use a calculator to evalua…

01:34

Okay. So for this example were asked to evaluate sign of 32 degrees by using taylor series. So in the textbook the taylor series for a sign of X is one half plus Route 3/2 X minus pi over six minus one quarter X minus pi over six squared plus additional terms. So this 32 degrees Great here. It can actually be rewritten as follows because we know that sign of 32 degrees is equal to sign of 30 degrees plus two degrees. And this can actually be written as sign of by over six plus by over 90. So essentially what we're gonna do is we're going to put this value in or X in our series. Okay. So we can say then that sign of 32 degrees is equal to. So we'll have one half plus route 3/2. Hi over six plus by over 90 minus pi over six minus one quarter. Oh one quarter. Hi over six plus pi over 90 minus pi over six square. So the Pie Over sixes will cancel. And that will just leave us with one half plus Route 3/2 by over 90 minus one quarter by over 90 squared. And we're gonna put this in our calculator and that will give us one half plus 0.3 017 minus 0.0 3043 Okay. And after adding these together, we'll get zero point 5299 And that is our answer.

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