On page 431 of Physics: Calculus, 2d ed., by Eugene Hecht (Pacific Grove, CA
Chapter 3, Problem 48(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 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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