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Use a linear approximation (or differentials) to estimate the given number.$ \cos 29^o $

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$\approx 0.875$

00:48

Amrita Bhasin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Missouri State University

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

04:22

Use a linear approximation…

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$23-28$ Use a linear appro…

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00:27

since 180 degrees equals pi radiance. What we know is that to get 29 degrees to radiance, we take, um, its value multiplied by pi and divided by 1 80. So we're gonna multiply these together and we get 29 pi over 1 80. So then we want to take the derivative using the definition of a derivative. Um so for this differential, what we'll have is f of X plus Delta X is approximately f of X plus delta X times F prime backs. So letting ffx being equal Thio cursing theater our coastline acts actually, um, Delta X being negative pi over 30 and X equaling pi over six. What we have is that the f of pi over six minus pi over 1 80 is equal to or approximately equal to f of high over six plus negative pi over 1 80 times f prime of pi over six. Now, we know that since, uh, f Prime of X is just equal to the negative sign of X that these values are going to change. This right here would just become times the negative sign of pi over six. Then, um what we want to dio is, since these are both positive or negative, will become positive. So when we evaluate this, we get Route three over to plus pi over 1 80 times one half This obviously make this 3 60 eso Our final answer for the cosine of 29 pie over 1 80 is going to equal route 3/2 plus pi over 3 60.

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