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JoshuaZ comments on Stupid Questions February 2015 - Less Wrong Discussion
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Yeah, this is completely historical. Edwards in his book on the Riemann zeta function tries to go back to using Gamma normalized in the obvious way so it agrees with factorial but that's never caught on.
In the case of the Riemann zeta function the key issue is that it is seen as more natural to have a plane of convegence for positive values of s. Moreover, writing it in that way, the values at positive integers are then natural and easy series.
Can you expand on this one?
It's a minor quibble. I think of cosine as the real part of e^ix, which is a very simple concept in my head. sine is the imaginary part of e^ix divided by i, which is slightly more complicated. If you had to relegate one to co- status, I'd choose sine.
Describing sine and cosine this way, instead of in terms of triangles, suddenly makes their behavior feel much more intuitive to me; on par with the way complex numbers in general suddenly made sense when someone here described multiplication by i as a rotation.
Thanks.
More elementarily: cos x and sin x are the x and y coordinates of the point on the unit circle at an angle x anticlockwise from the positive x-axis. (I think this is the correct version of the "triangles" definitions.)
If you don't rotate, the cosine is still there; only the sine is zero. So, in some sense, cosine is more fundamental; it was there before the rotation.