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On page 431 of $ Physics: Calculus, $ 2d ed., by Eugene Hecht (Pacific Grove, CA: Brooks/ Cole, 2000), in the course of deriving the formula $ T = 2\pi \sqrt {L/g} $ for the period of a pendulum of length $ L, $ the author obtains the equation $ a_T = -g \sin \theta $ for the tangential acceleration of the bob of the pendulum. He then says, "for small angles, the value of $ \theta $ in radians is very nearly the value of $ \sin \theta; $ they differ by less than $ 2\% $ out to about $ 20^o." $(a) Verify the linear approximation at 0 for the sine function:$ \sin x \approx x $(b) Use a graphing device to determine the value of $ x $ for which $ \sin x $ and $ x $ differ by converting from radians to degrees.

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Baylor 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.

03:45

On page 431 of Physics: Ca…

04:46

01:57

02:54

07:24

A simple pendulum consists…

04:19

The figure shows a pendulu…

12:56

12:10

Hi, what its the answer fo…

okay, part ay. So the first thing we know is that we can use the Formula 000 plus f prime of zeros one times X minus zero, which gives us acts. So Olive Axe is simply equivalent to X copping for my graphing calculator. Now we know we have X minus Sign axe over. Sign X is 0.2 So to figure out where this equals again using a graphing calculator, we get closer minus your 0.344 times 1 80 over pie gives us 19.7 degrees. So, in other words, remember, this is between negative 0.3440 point 344 because it's plus or minus 3440.344

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