# [Python-ideas] Fwd: Trigonometry in degrees

Ronald Oussoren ronaldoussoren at mac.com
Mon Jun 11 04:00:17 EDT 2018

```Op 11 jun. 2018 om 09:18 heeft Jacco van Dorp <j.van.dorp at deonet.nl> het volgende geschreven:

>> Remember, because π is irrational, we cannot actually call sin or cos on
>> any rational multiple of π. We can only operate on multiples of pi,
>> which is *close to* but not the same as π. That's why it is okay that
>> tan(pi/2) returns a huge number instead of infinity or NAN. That's
>> because the input is every so slightly smaller than π/2. That's exactly
>> the behaviour you want when x is ever so slightly smaller than π/2.
>
>
> This would basically be the reason for a PiMultiple class - you can
> special case it. You'd know sin(PiMultiple(0.5)) == 0. You'd know
> cos(PiMultiple(0.5)) == -1 and tan(PiMultiple(0.5)) == nan. This could
> let you remember as much angles as possible into multiples of pi, and
> as long as you're in multiples of pi, you're exact.
> PiMultiple(Fraction(1, 6)) would be exact and could give the right
> sin() and cos() behaviour.
>
> And because it'd be a numeric type, you could still use it with all
> other numeric types and add/multiply etc it. When you add and subtract
> it with another numeric type, it'd lose the special status, but even
> with multiples and divisions you can preserve it's specialness.
>
> And if it gets weird values, you can always fall back on converting it
> to a float, therefore never giving worse results.
>
> It also gives a reason -against- degrees. if you have PiMultiple or
> TauMultiple, it's rather easy to give common angles, and students can
> learn to properly learn radians for angles as they should.(because,
> lets be honest, they're objectively better measures of angles than
> degrees, or even *shiver* grads. )
>
> We SHOULD make it easy to code exact and the right way, and I think a
> PiMultiple class could help that a lot. That said, it does need a
> better name.

What is the real world advantage of such a class?  So far I’ve only seen examples where the current behavior is said to be confusing for students.  In most cases where I have used math.sin the angle wasn’t a constant and wasn’t an exact mulltiple of pi.

Ronald
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