[Python-ideas] Trigonometry in degrees

Stephen J. Turnbull turnbull.stephen.fw at u.tsukuba.ac.jp
Fri Jun 8 01:37:33 EDT 2018

```Richard Damon writes:

> To make it so that sindeg/cosdeg of multiples of 90 come out exact is
> probably easiest to do by doing the angle reduction in degrees (so the
> nice precise angles stay as nice precise angles) and then either adjust
> the final computation formulas for degrees, or convert the angle to
> radians and let the fundamental routine do the small angle
> computation.

You would still need some sort of correction for many angles because
of the nature of floating point computation.  The modern approach is
that floating point is exact computation but some numbers can't be
exactly represented.  Since Pi is irrational, Pi/4 is too, so it
definitely cannot be represented.  Making a correction to a number
that "looks like" Pi/4 is against this philosophy.  So you need
separate functions (a "high school mode" argument would be frowned
upon, I think).

> While we are at it, it might be worth thinking if it might make sense to
> also define a set of functions using circles as a unit (90 degrees =
> 0.25, one whole revolution = 1)

While 1/4 is no problem, 1/6 is not exactly representable as a binary
floating point number, and that's kind of an important angle for high
school trigonometry (which is presumably what we're talking about here
-- a symbolic math program would not represent Pi by a floating point
number, but rather as a symbol with special properties as an argument
to a trigonometric function!)

My bias is that people who want to program this kind of thing just
need to learn about floating point numbers and be aware that they're
going to have to accept that

>>> from math import cos, radians
6.123233995736766e-17
>>>

is good enough for government work, including at the local public high
school.

Of course, I admit that's a bias, not a scientific fact. :-)

--
Associate Professor              Division of Policy and Planning Science
http://turnbull.sk.tsukuba.ac.jp/     Faculty of Systems and Information
Email: turnbull at sk.tsukuba.ac.jp                   University of Tsukuba
Tel: 029-853-5175                 Tennodai 1-1-1, Tsukuba 305-8573 JAPAN
```