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grayrat187Lv1
28 Apr 2020
On page 431 of physics; Calculus 2d ed. by Eugene Hecht (Pacific Grove: Brooks/Cole 2000), in the course of the deriving the formula
for the period of a pendulum of length
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 radius is very nearly the value of
; they differ by less than 2% out to about
.’’
(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 Hecht’s statement by converting from radians to degrees.
On page 431 of physics; Calculus 2d ed. by Eugene Hecht (Pacific Grove: Brooks/Cole 2000), in the course of the deriving the formula for the period of a pendulum of length 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 radius is very nearly the value of; they differ by less than 2% out to about.’’
(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 Hecht’s statement by converting from radians to degrees.
Jamar FerryLv2
22 May 2020