Re: [math-fun] True or False, Log[Tan[t + π/4]]
is an odd function of t? ----- It's pretty darn strange, no doubt about it. —Dan
Assuming you mean log(tan(t+pi/4)), this is igd(2t), inverse gudermannian of 2t, which is an odd function for small t. To see this without appealing to special functions, notice that (switching to degrees) tan(45+x) = cot(45-x) since the angles sum to 90. Using cot == 1/tan, and applying the log, we get log(tan(45+x)) = - log(tan(45-x)). Rich ------- Quoting Dan Asimov <dasimov@earthlink.net>:
is an odd function of t? -----
It's pretty darn strange, no doubt about it.
?Dan
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f(x) = log(tan(x + pi/4)) = log((cos(x) + sin(x))/(cos(x) - sin(x))) f(-x) = log((cos(x) - sin(x))/(cos(x) + sin(x))) = -log((cos(x) + sin(x))/(cos(x) - sin(x))) = -f(x) and f is an odd function.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Wednesday, July 27, 2016 10:16 PM To: math-fun Subject: Re: [math-fun] True or False, Log[Tan[t + π/4]]
is an odd function of t? -----
It's pretty darn strange, no doubt about it.
—Dan
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