Solved: On page 431 of Physics: Calculus, 2d ed., by Eugene Hecht (Pacific Grove, CA

Chapter 3, Problem 3.10.42

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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 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 inradians is very nearly the value of ; they differ by lessthan 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 forwhich and differ by less than 2%. Then verifyHechts statement by converting from radians to degrees.

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