Re: Avoid the use of certain functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg111108] Re: Avoid the use of certain functions*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Tue, 20 Jul 2010 03:45:30 -0400 (EDT)

One should not be so quick to condemn the world when it does not conform to your own preconceptions and preferences! There is a good geometric reason that sec is an appropriate name for the reciprocal of cos rather than of sin. Draw the unit circle, center at the origin O. Mark off a central angle of theta from the positive x-axis, and let P be the corresponding point on the circle. Draw the vertical line L through the point (1,0). Extend the ray OP until it intersects L at a point Q. Then the length of OQ is sec (theta). That line segment OQ cuts across the circle. [See, e.g., http://en.wikipedia.org/wiki/Trigonometric_functions. (I thought I remembered also some Wolfram Demonstration of this, but I cannot locate it now.)] Furthermore, in the usual list of the 6 trig functions sin cos tan cot sec csc there is a symmetry of pairs around the middle: cot = 1/tan, sec = 1/cos, csc = 1/sin. Finally, what's wrong with sec and csc? Mathematical expressions are often simpler when expressed in terms of them, since this avoids (explicit) use of fractions for the functions. On 7/19/2010 2:10 AM, AES wrote: >> From: Sam Takoy [mailto:sam.takoy at yahoo.com] >> >> Hi, >> >> Is there a way to ask Mathematica to avoid expressing answers in terms >> of certain functions. For example, I [can't?] stand Sec, Csc, Sech, and Csch >> and would rather see Sec^-1, etc. > > I'm with you on this one: always hated Sec and Csc (and never > understood the backward naming of these functions -- why isn't Sec = > 1/Sin and Csc = 1/Cos?) > > So, I'd like the various Simplifiy and XxxToYyy functions in Mathematica to > always give precedence to Sin and Cos by default, and avoid using Sec > and Csc whenever possible, even if this produces some "1 overs" in the > output expression. > > But I suspect trying to implement this at this point would require more > complexity than it would be worth. > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305