On page 431 of Physics: Calculus, 2d ed., by Eugene Hecht
Chapter 3, Problem 3.593(choose chapter or problem)
On page 431 of Physics: Calculus, 2d ed., by Eugene Hecht (Pacific Grove, CA: Brooks/Cole, 2000), in the course of deriving the formula for the period of a pendulum of length L, the author obtains the equation aT !%t sin (for the tangential acceleration of the bob of the pendulum. He then says, for small angles, the value of in radians is very nearly the value of ; they differ by less than 2% out to about 20. (a) Verify the linear approximation at 0 for the sine function: ; (b) Use a graphing device to determine the values of for which and differ by less than 2%. Then verify Hechts statement by converting from radians to degrees
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