# [Python-ideas] Trigonometry in degrees

Steven D'Aprano steve at pearwood.info
Fri Jun 8 21:12:35 EDT 2018

```On Fri, Jun 08, 2018 at 11:11:09PM +0200, Adam Bartoš wrote:

> But if there are both sin and dsin, and you ask about the difference
> between them, the obvious answer would be that one takes radians and the
> other takes degrees. The point that the degrees version is additionally
> exact on special values is an extra benefit.

No, that's not an extra benefit, it is the only benefit!

If we can't make it exact for the obvious degree angles, there would be
no point in doing this. We'd just tell people to write their own
two-line functions:

def sindeg(angle):

The only reason to even consider making this a standard library function
is if we can do better than that.

> It would be nice to also fix the original sin,

The sin function is not broken and does not need fixing.

(Modulo quirks of individual platform maths libraries.)

> or more precisely to provide a way to give it a
> fractional multiple of pi. How about a special class PiMultiple that would
> represent a fractional multiple of pi?

What is the point of that? When you pass it to math.sin, it still needs
to be converted to a float before sin can operate on it.

Unless you are proposing a series of dunder methods __sin__ __cos__ and
__tan__ to allow arbitrary classes to be passed to sin, cos and tan, the
following cannot work:

> PI = PiMultiple(1)
> assert PI / 2 == PiMultiple(1, 2)
> assert cos(PI / 2) == 0

Without a __cos__ dunder method that allows PiMultiple objects to
customise the result of cos(), that last line has to fail, because
cos(math.pi/2) == 0 fails.

> DEG = 2 * PI / 360
> assert sin(45 * DEG) == sqrt(2) / 2

Likewise.

--
Steve
```