<Whenever I get the inquiry about why we use radians, the simplest
way to answer that beginning user is to ask them to find the length of arc
of a circle of radius 3 subtended by a central angle of 13 degrees (or use
some other numbers that aren't factors of 360). The point soon becomes
quite clear that if the central angle is defined as the ratio of arc to
radius, life is simpler and more meaningful.>
I'm not sure how much more simpler life is. If I'm measuring in degrees =
then I have to multiply 2 pi times the radius 3 times 13/360 to find out =
that the length of the arc is about .68 inches. If I measure in radians, =
I have to convert 13 degrees to radians by multiplying 13 times pi /180 =
times 3 inches to find that the length of the arc is .68 inches. The =
computations are virtually identical---what was simpler?
< Another nice example is to simply ask them to graph y =3D x - =
sin(x)
and make some sense of it. It is a nice way to see that for x >=3D 0, y =
is
positive, but not by much for small x, which shows why linear approximation=
works so well near x =3D 0.>
I don't understand the relevance of this for my pre-calculus students. =
Why should they be interested in the linear approximation near zero? And =
if they were and they left their calculators in degree mode then the =
linearization would be (180/pi) times x. So what?
l
-----Original Message-----
From: Martin Kalmar [mailto:MKalmar@fcc.cc.md.us]=20
Sent: Monday, Nov
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