Re: Circle of Confusion Question

From: Sandy King <sanking@clemson.edu>
Subject: Circle of Confusion Question
Date: Sun, 08 Aug 2004 19:53:21 -0400

> He provides the answer for this equation for a distance of 25 cm as a
> linear measurement of 0.07mm, or 70 microns, and continues by noting
> that the tangent of one minute of arc is roughly 0.00029. I have
> worked this problem backwards several ways and still have not been
> able to figure out how he determined that the tangent of one minute
> of arc is 0.00029.

What did you get? If you got tan 0.0167 = 0.0167, I suppose your
calculator used radian as the unit of the angle while you assumed it
was degree. You need to change the calculator's setting, or convert
the unit before obtaining tangent. 180 degrees is exactly one pi
radian.

For such a small value like 1/60 of a degree, tan x is practically x
where x is in radians. (That is, if alpha is the angle in degrees,
tan alpha is very close to alpha/57.3.) This is obvious if you obtain
Taylor series expansion of tan x around x = 0 (or Maclaurin
expansion).

--
Ryuji Suzuki
"You have to realize that junk is not the problem in and of itself.
Junk is the symptom, not the problem."
(Bob Dylan 1971; source: No Direction Home by Robert Shelton)