(a) The accompanying figure shows a sector of radius r and central angle 2 α . Assuming that the angle α is small, use the local quadratic approximation of cos α at α = 0 to show that x ≈ r α 2 / 2. (b) Assuming that the Earth is a sphere of radius 4000 mi, use the result in part(a) to approximate the maximum amount by which a 100 mi arc along the equator will diverge from its chord.
(a) The accompanying figure shows a sector of radius r and central angle 2 α . Assuming that the angle α is small, use the local quadratic approximation of cos α at α = 0 to show that x ≈ r α 2 / 2. (b) Assuming that the Earth is a sphere of radius 4000 mi, use the result in part(a) to approximate the maximum amount by which a 100 mi arc along the equator will diverge from its chord.
(a) The accompanying figure shows a sector of radius
r
and central angle
2
α
.
Assuming that the angle
α
is small, use the local quadratic approximation of
cos
α
at
α
=
0
to show that
x
≈
r
α
2
/
2.
(b) Assuming that the Earth is a sphere of radius 4000 mi, use the result in part(a) to approximate the maximum amount by which a 100 mi arc along the equator will diverge from its chord.
Precalculus: Mathematics for Calculus - 6th Edition
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